23. Future Experiments - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

In our effort to characterize the dark side, we've recently focused on where the universe came from, the laws of string theory, the Multiverse, extra dimensions, etc. These may help us to determine the natural values of dark matter and dark energy, but thinking can only go so far, so we need to go beyond our current understanding by means of experiments.

Special Relativity and Newton's gravity led us to General Relativity. Quantum mechanics and General Relativity led us to string theory. Yet experimentation will lead us to something even better. Our standard model of particle physics could be thought of as being too good. We need more experiments in order to be able to come up with something better. The concordance cosmology of 5% ordinary matter, 25% dark matter, and 70% dark energy is a victory, but we need much more to characterize the dark side.

When we learn more, there are more chances when sometime we may find great surprises. The supernovae observations surprised us with the accelerating universe. Who knows what other surprises await us? I like this point by Sean and I hoped he would expand on it much more than he did. Maybe in the last lecture of the course? This all points to the need for more observations.

So far, our observations have been strictly of photons, with only a minute fraction otherwise. Photons have enabled our discovery of energy density to explain the flatness, or dark matter to explain the structure, of the universe. But with improved resolution we can discover much more.

The CMB observations provided great returns when mapped out at a one degree resolution. But we can go to smaller scales for new returns. The Planck Surveyor in 2008 should tell us the amount of dark matter, ordinary matter and more sensitive fluctuations. The intrinsic polarization of the universe has been detected, but gravity waves from inflation may be detected. The somewhat vanilla predictions of flatness and homogeneity could be improved by tensor predictions from inflation.

Large scale observations are also improving. The SDSS returned one million redshifts and is complemented by 250,000 from 2DF. Combine these with the lensing surveys where weak lenses affect shapes of galaxies, and we have a map of all the stuff in the universe. The LSST around 2013 in Chile will observe the entire sky each night. This massive archive will need help from Google to just browse the catalog. Large scale structure, lensing, supernovae, and potentially dangerous near earth asteroids are all on the observing schedule.

Clusters of galaxies will help with the number density of the universe. The Sunyaev-Zeldovich effect is the shadow created when the CMB goes into a cluster, scatters off the gas, and does not then come to us. The spot left in the CMB is observable and is a good measurement of all galaxies in that region of space. The South Pole Telescope is one such project, but will need to be followed up by x-ray observations. Since dark energy actually prevents more clustering in the universe, the number of galaxies is a good way to measure the dark energy.

The last photon observations in our list, is of gamma rays. When dark matter annihilates there would be gamma rays produced. GLAST could detect them in late 2007.

Neutrinos are the first non-photon observations we'll talk about. So far only the sun and SN1997a have been observed in neutrinos. The nature of neutrinos is one of light mass and mixing into one another, thus solving the solar neutrino problem. But there could be new kinds of neutrinos like sterile that only interact with gravity and each other.

Gravity waves are weak but could be detected by LIGO, now that data is coming in at the intended rate. The LISA satellite observes a different wavelength than LIGO, where spiraling black holes could be used as the next standard siren. This is a clean idea without the messy problems of photon physics.

Dark matter could be detected on Earth by CDMS in a Minnesota mine or DAMA in Italy. The latter claimed a positive detection, but not many believe it. It could be a new kind of dark matter, which is the very point of making such observations to start with.

The Cassini mission has confirm the expected time delay of radiation caused by gravity. The STEP satellite is a high risk but high payoff experiment for testing equivalence. The inverse square law is being tested at sub millimeter scales.

Dark matter and dark energy need explaining from particle physics, which means going beyond the standard model. The axion or supersymmetry options for dark matter, and the quintessence, vacuum energy, or worse, options for dark energy, are all open to new particle physics research. Fermilab's Tevatron and CERN's LHC will open a new realm in 2008 for the Higgs Field, supersymmetry, or even extra dimensions and completely new phenomena.

We've set ourselves the task of understanding the dark side of the universe, the dark sector that makes up 95% of the stuff we seem to have in our contemporary cosmology. For the last few lectures, our strategy for understanding the dark sector, has been to think really hard about where the universe came from, and how inflation could have taken us from a tiny patch to the big universe we see, and to think about how the fundamental laws of physics work, in terms of the possible roll of string theory, extra dimensions, and the multiverse.

These ideas come into our conception of dark mater and dark energy, because they give us a framework in which to think about what are natural values for different things to have. What is the natural value for the dark matter to be, for the dark energy to be, etc?

Thinking hard is great, and sometimes it's all you have. Yet experiments and data are always better. In either case, what we're trying to do, is to go beyond our current understanding. Sometime you do that because your current understanding is mutually inconsistent with itself. Special Relativity and Newtonian gravity were inconsistent, then Einstein used that to invent General Relativity. Now we have quantum mechanics and General Relativity being inconsistent, and that's how we get to string theory.

Yet it's never as good as actually having a piece of data that says your current theory is wrong. Part of the reason why we have not had great progress in particle physics in the last 30 years, is because the standard model is too good! It fits all the data really well. To move beyond and get a better idea of what's going on next, it is always better to go a new, experimental piece of information, which doesn't fit our current theory.

So the good news is we have a huge amount of experiments coming online in the next few years, which hopefully will teach us more beyond what we already know. Sean reminds us, though we've probably heard it too often by now, that we have a model that fits the data. We have a picture of the universe in which 5% is ordinary matter, including particles from the standard model of particle physics, 25% is dark matter, and 70% is dark energy.

The dark matter is some particle that is massive, moves slowly, and doesn't interact very strongly, while the dark energy is some form of energy that is smoothly spread through space and slowly evolving through time. So that's fine, that's a model that fits the data we have. Yet should we therefor declare victory? If we stopped collecting more data, we wouldn't have any discrepancies!

Yet we want more than that. We want to understand what is going on. Even though we know there is dark matter and that there is dark energy, we don't know what these things are, so we're going to push our experiments forward. Remember that when we do so, sometimes we learn a little bit more about what we were studying, yet sometimes we're completely surprised.

One of the supernovae groups that tried to measure the deceleration of the universe, titled themselves as "measuring the deceleration." Yet they actually discovered the acceleration! Those are the best kinds of experiments. So even though we can talk about what kinds of experiments we'll be doing over the next few years, we cannot talk about what we'll learn from them. We have things we hope to learn, but we need to keep an open mind and maybe we'll be surprised.

So we can characterize the kinds of experiments we'll be doing, by the kinds of things we'll be looking at. In other words are they looking at photons, neutrinos, or what have you? Photons, of course, are a favorite way to look at the universe, they always have been. So we'll start by looking at what we can learn by measuring photons coming from the sky. There's also photons we can make here on the ground of course. Traditionally, all of astrophysics and astronomy, by default meant studying photons you get from the sky. Photons across the electromagnetic spectrum, from radiowaves at very long wavelengths, through microwaves and infrared, up to visible photons that we see with our eyeballs, and then to shorter and shorter wavelengths through ultraviolet, x-rays, and ultimately to gamma rays.

It says something about the state of our progress that we even make a meaningful distinction between looking at the sky in photons versus anything else! For the first time in human history, in the last couple of decades we've begun to look at the sky in other kinds of ways. Yet nevertheless, it's still photons that give us the overwhelming amount of our information.

You might think we could organize the kinds of experiments we're going to be doing, by what kinds of photons we'll be looking at, x-rays versus ultraviolet for example. However it turns out that for some kinds of objects in the sky, they are best understood by looking at the same object in different wavelengths. Therefor lets organize how we'll be looking at the universe by what we'll be looking at, rather than by what wavelength of photon we'll be using. So lets go from the largest things in the sky to the smallest.

The largest thing really, is the CMB, the leftover radiation from the Big Bang, a snapshot of what the universe looked like about 400,000 years after it began. It's the tiny variations in temperature that the CMB has in place to place within the sky, that teach us a tremendous amount about what the early universe was really like. It's already been a treasure trove of information about what the universe was like then, and what it must be like now. We've learned from the temperature fluctuations in the CMB, first that space is flat. Therefor, if the Friedmann equation is right, you need enough ρ to account for a spatially flat universe. Secondly, we've learned that ordinary matter is not enough. In order to explain the different sized splotches of hot and cold that we see in the CMB, it's necessary to introduce stuff other than ordinary matter and that of course, is the dark matter.

So what will we learn by going beyond what we've already done with the CMB? Well the first thing we can do is the most obvious, which is we can get better resolution, we can look at smaller angular scales. The most interesting angular scale, if you have to pick one on the CMB, is about one degree. That one, we've pretty much mapped out. Yet there could be surprises awaiting us at smaller and smaller scales. One prediction of inflationary cosmology is not just that there are perturbations at early times, but relationships between the amount of perturbations at different wavelengths, at different distances on the sky. So a big project for the future would be comparing fluctuations of large angles on the sky, to what fluctuations looked like at smaller angles.

To do that, we have a satellite supposed to be launched by 2008 called the Planck Surveyor, after the German astrophysicist Max Planck. It will give unprecedentedly accurate views of what the CMB looks like at very tiny angles. We'll get from that, a high precision way of measuring the cosmological parameters. Not just how much dark energy there is, but how much dark matter, ordinary matter, and the kind of fluctuations of the early universe which grew into the galaxies and structures we observe today.

Yet even then, we won't be done with the CMB. We're still going to try and squeeze more information out of it. We've already mentioned that we've discovered the polarization of the CMB. The wavelengths we're getting from the CMB, are polarized in different directions, depending on the temperature fluctuations. Yet in addition to the intrinsic polarization we've already observed, there's an additional component, hypothetically, due to gravitational weaves created by inflation.

These have not yet been observed. One of the major upcoming projects, hypothetically in a satellite mission, will be a dedicated search for the polarization imprint of gravitational waves from inflation. If you could find those, and they had the properties that were predicted by our currently favored models of inflation, that would be the best evidence we know how to get that something like inflation that was true in the early universe.

Right now we have models of inflation that are consistent with everything we observe, yet their prediction are kind of vanilla. They're that the universe should be flat, that the perturbations should be approximately the same on all scales. The tenser perturbations, which are what we call the perturbations you get from gravitational waves, are a specific and quantitative prediction from inflation. So if that turned out to be right, you'd really think we were on the right track.

After the CMB, the next largest thing we can look at is large scale structure in the universe. In other words we can map out the stuff that you see in the later universe, the stuff you see in clouds and dust. Right now the state of art is something called the SDSS (Sloan Digital Sky Survey), along with a slightly smaller survey called the 2DF (Two-degree Field Galaxy Redshift Survey). The SDSS has about 2 million redshifts for galaxies, collected at a telescope in Arizona, while the 2DF has about 250,000 redshifts collected from Australia.

Together they've given us unprecedented views of the way in which structure stretches across the universe. So by matching the CMB, which is a snapshot of the universe 400,000 years after the Big Bang, to such redshift surveys, which are snapshots of the universe 14 billion years after the Big Bang, we're beginning to piece together how structure has evolved from early times to late times.

That is a messy and complicated astrophysical problem. Even if you knew from inflation what the initial perturbations were, and you knew the ingredients of the universe in terms of dark matter and dark energy, it's still quite a bit of work to trace, from those initial perturbations, to what we see today. So there's a lot of dirty, important astrophysics that needs to be done, and observations of the distribution of structure are going to be crucial to make sure we're on the right track when doing that.

One of the most important roles of redshift surveys of galaxies across the sky, will not simply be to use those data all by themselves, but to compare them to other kinds of data. So one thing we'll be doing is surveys of gravitational lensing. Only very recently have we been able to develop cameras that can take images of what's on the sky, to such precision that you can tease out the slight perturbations of the shapes of galaxies due to gravitational lensing. It's the weak lensing that's going to be a treasure trove of information for future cosmologists. Remember that if gravitational lensing happens, the beam of light we get from a background galaxy is reflected by some mass distribution, and by the amount of deflection you can measure how much mass there is. That's more or less the basic picture if you're lucky enough to get the object acting as a lens, one background object that you observe on the sky.

The real universe of course, has many galaxies in it, many clusters of galaxies, all in a messy configuration. That's bad if you only want to take one picture and get one piece of information, but we're learning how to use that messiness to our advantage. We're now learning how to make 3D maps of where the stuff is in the universe, using the amount of gravitational lensing that is undergone by galaxies at different redshifts. So by combining redshift surveys that tell us where the galaxies are in space, with lensing surveys that show us how their images are distorted on the sky, we're mapping out where the stuff is in the universe.

This is something first done in 2007, a technique we'll be perfecting and improving just a few years from now. The great leap forward in doing these kinds of surveys will be something called the LSST (Large Synoptic Survey Telescope). This has been on the drawing board for quite a while now, and will be for some time to come. It is supposed to start construction in 2010, be finished by 2013, being built in the mountains in Chile where the air is very thin for the best view of the sky. The goal is to survey a large patch of the sky every single night.

So what something like the SDSS can do over the course of years, is to take images of different patches of the sky, and piece them together into an image of what is going on. The LSST will basically be doing that everyday. So it will be collecting a huge amount of data, unprecedented in astrophysics, over a petabyte of data per year! So just as a gigabyte is 1000 megabytes, a terabyte is 1000 gigabytes, and a petabyte is 1000 terabytes. So one petabyte is the equivalent of 250 billions songs on your ipod, a huge amount of data, so much so that just surfing through the data, looking for different pieces of information, is an incredibly difficult computer science problem.

In fact, we'll not be surprised to learn that scientists working on the LSST project, are collaborating with researchers from Google, who are the best people in the world for searching through large databases and finding things. So astronomers want Google's technology to search through their database, while Google wants the data astronomers have, because they are the only ones in the world who collect huge amounts of data and then give it away for free.

So what we'll be getting from LSST is huge amounts of data, where lensing will be an important goal to be able to look for the 3D structures of the universe. Yet we'll be looking at the same region of the sky, over and over again. In other words we'll be collecting data in the time domain, something astrophysicists have traditionally not done because it's just to expensive. In other words, we'll not just get weak lensing and large-scale structure, but also discover supernovae and asteroids coming to crash into the earth. This is a major funding source for the LSST, to find objects in the solar system that might be of danger to us. It doesn't tell us anything about dark matter and dark energy, but it's still a useful goal.

So going to smaller and smaller things in the universe, next lets consider clusters of galaxies. Remember that clusters are, on the one hand, the largest bound structures in the universe, yet on the other hand they are a fair sample of what is in the universe. So by studying clusters so far, we've been able to learn about the relative proportions of lets say, dark matter to ordinary matter in the universe.

The new thing we'll start doing with clusters of galaxies, is to count them. By counting the number density of stuff in the universe, you're tracing out how it has evolved. People have always known this to be true, yet historically this is a very difficult technique to use, since when you're counting things it's crucially important that you don't miss anything. In astrophysics, some things are bright, some are dim. When you try to count things, you don't know you've found all of them, but clusters of galaxies are special.

In a cluster, galaxies fall together, gas and dust falls in along with them, and it heats up. There's something called the Sunyaev-Zeldovich effect, in which it's not that we're looking at the gas, but at the shadow cast by this hot gas, on the CMB. So you look at the CMB in the sky, and look for a little dot on it, a little dark spot. This is caused by the fact that the photons from the CMB come into the cluster, scatter off the gas, and don't get to you. The reason why this is important is that since you were looking at the light emitted by the cluster, it would become dimmer as you get further away. So it's harder to find clusters that are far away.

Yet if you're looking at the shadow cast by the cluster, it's just a shadow, so it doesn't get any dimmer the further away you get! So by doing a survey for the Sunyaev-Zeldovich effect, we'll be able to find all the clusters of galaxies in the patch of sky on which you're looking, which will be an unbiased sample of all the clusters of galaxies in some region of the universe. We are currently doing that with something called the South Pole Telescope, a ten meter radiotelescope set up in Antarctica in the south pole, that starts operation in 2007. Once it finds these clusters of galaxies, we'll follow that up with x-ray observations that will allow us to weigh the clusters, to measure how much mass is in them.

Yet more importantly, it's the number of clusters of galaxies that count. As the dark energy making the universe expand, takes over, it stops structures form forming. When you have a matter dominated universe, the matter gradually collects together and forms bound structures. Yet when the dark energy takes over, the matter is pushed apart and galaxies stop falling together. So the number of clusters of galaxies as a function of distance in the universe, is a very sharp way of figuring out how much dark energy there is. It is arguably competitive with supernovae and other measurements. We don't know yet, since we don understand the fundamental physics of galaxy clusters very well, but that's something that numerical simulations are teaching us about right now.

Meanwhile of course, we're not done with supernovae. They are the way we discovered the dark energy in the first place, and we want to do better. The important role there is that we'd like to understand the fundamental intrinsic nature of the supernovae themselves. If you collect enough examples, so that instead of 20-40 supernovae, you have 1000, then you can start talking about what the distance-redshift relationship is for each individual possible kind of supernovae. What it looks like for supernovae in elliptical galaxies, spiral galaxies, and so forth. You can search for possible systematic effects that might put you on the wrong track.

By doing this, we'll be able to measure the equation of state parameter of the dark energy. It's what we called w, and will be -1 if the dark energy is truly constant, and something like -0.8 or -0.9, if it's a gradually declining quintessence. So looking for supernovae at very high redshift, is our best hope for figuring out whether the dark energy is truly constant or slowly varying.

Finding supernovae at large distances is hard if you're here on earth. Therefor there are proposals to build a dedicated satellite to do exactly that. Right now the plans are for NASA and the DOE to team up and build JDEM (Joint Dark Energy Mission). However Sean can't promise us it will be built, since these things depend on Congress, money, and other things that scientists don't have much control over.

Finally in terms of looking at photons, we can look at gamma rays for indirect evidence of dark matter. That is to say, we have dark matter particles in the universe, so we can of course look for them here on earth, but also in the sky by waiting for dark matter particles and anti-particles to annihilate. If the dark matter is a WIMP, then the real dark matter density comes from both particles and anti-particles. Occasionally they are going to annihilate and give off gamma rays. Right now we don't have much of a capability for looking at gamma rays in the sky, but the new GLAST satellite is scheduled to be launched in late 2007, which will give us our first direct view, and might be an indirect detection of dark matter.

Of course those are not the only particles we use. We don't only use photons to look at the universe, we use other particles like neutrinos. For example, we use neutrinos. Ever since the solar neutrino problem that was noticed in the late 60s and early 70s, we've been able to find neutrinos from outer-space, not just from here on earth. Besides the sun, the one kind of neutrino we've been able to detect from outer-space are neutrinos from SN1987a.

So one of the things that neutrino physicists have been doing, is planning for the next supernova. They're ready to get even more information about fundamental neutrino properties from whatever supernova goes off next in our own galaxy. We don't know when that's going to be, but it typically happens once every hundred years, so you never know.

Meanwhile we'd like to learn more about the fundamental nature of neutrinos, which has recently opened up as a growth field in physics. We now know the neutrinos have mass, they are very light, but do have some mass. Because they do, they can mix. In other words, we said there were things called electron neutrinos, muon neutrinos, and tau neutrinos. Yet they all can change into one another as long as they have mass. This has been experimentally found, and is the kind of thing we're trying to better understand.

The role for dark matter is that none of the three neutrinos we know and love, can be the dark matter. Yet there could be others, kinds we haven't yet directly detected. For example, sterile neutrinos which do not interact with W and Z bosons. The only way sterile neutrinos interact is through gravity and with other neutrinos. So we're trying to build neutrino detectors that will be able to tell the difference between sterile neutrinos and ordinary neutrinos, since that might play an important role in the dark matter mystery.

Getting more exotic, we can look at gravitational waves. Just like electromagnetic waves arise from electric charges moving up and down, gravitational waves are created when heavy objects move back and forth. For example, if you have two objects orbiting each other, they will be emitting gravitational waves.

Now, gravity is a very weak force, so these waves are not very easy to notice. We have never yet directly detected gravitational radiation. We do have an observatory that is trying to do exactly that. We have LIGO (Laser Interferometer Gravitational Wave Observatory), which finally right now by 2007is finally collecting data at the rate it was designed to do. It has not yet detected any objects, and it may not even succeed in doing so.

We have a batter plan for a gravitational wave observatory in space, called LISA (Laser Interferometric Space Antenna). This would include three satellites, 5 million km apart from each other, that look for gravitational waves in a completely different wavelength than LIGO was looking, which is actually good news for cosmology. One of the things LISA will be looking for, is if you have a tiny black hole orbiting a supermassive, million solar-mass, black hole, it will be orbiting, spiraling, and giving off gravitational waves all along.

It turns out that just like supernovae are standard candles, in-spiraling black holes can be standard sirens! You can learn enough about the parameters of the black hole binary, to figure out how much gravitational waves were given off at the source. So by detecting them here and measuring how strong the waves appear to us, we can figure out how far away it is. This is a completely independent way of measuring distances in cosmology. It's also a very clean way, one that doesn't get messed up with the messy astrophysics that ordinary objects giving off photons do. If we can turn standard sirens into a useful cosmological tool, we'd be able to get unprecedented precision in mapping out the expansion of the universe, out to very distance redshifts.

Next up we have dark matter. Remember that we can look for this by using photons, at the gamma rays that are emitted when dark matter and "anti-dark matter" particles come together. Yet of course, we can also look for dark matter right here on earth. We can build underground detectors that will wait for a dark matter particle to come in, bounce off a nucleus in the detector, and leave a little bit of energy there. We have detectors working right now, though unfortunately we don't have a very precise prediction for when we'll be able to observe them. There's a lot of freedom in the predictions there, so we can't say by which year we should be able to detect things, but it could very well be any moment.

There's a detector called CDMS (Cryogenic Dark Matter Search) which is underground in Minnesota and working right now. It currently has the world's best limits. There's another detector called DAMA is Italy, which works on an interesting system where it doesn't look for the total amount of signal, but for the variation in signal throughout the year, as the earth revolves around the sun, and moves through the dark matter cloud around it. We mention DAMA because it has claimed to have found a signal. They claim they have already detected the dark matter. Yet the reason why this isn't earth shattering news is because most people don't believe them. The current consensus in the dark matter detection communities is that they have some systematic error they haven't yet detected.

Yet there is an interesting alternative possibility, in that there could be a new kind of dark matter, some specific particle physics model which shows up more easily in something like DAMA than something like CDMS and the other detectors. In other words, this is why we do experiments, since the real world might be more complicated than the simple models we write down! So stay tuned for news from dark matter detection experiments, we might be very quickly learning important feature about 25% of the universe.

So coming in closer to home, besides looking at things in the sky, we can also do experiments closer by. Before, ordinarily, closer by would mean here on earth in the lab. Yet these days you have to extend it to at least the solar system. We can send satellites throughout the solar system to help us do physics experiments. The most obvious example is testing General Relativity. We already mentioned the Cassini mission which had as its primary goal, to take pictures of Saturn, Jupiter, and the other outer planets, yet it also tested General Relativity by sending signals to us that we used to measured the time delay.

There are new upcoming missions that will also test General Relativity. There is something called the STEP mission (Satellite Test of the Equivalence Principle), which will be asking if different objects made of different stuff, move differently in a gravitational field. Remember a very firm prediction of General Relativity is that everything responds to gravity in exactly the same way. That is known as the equivalence principle.

If there is some fifth force, some new light field that stretches out over macroscopic distances, it will show up as a violation of the equivalence principle. Quintessence might be exactly such a field, we don't know. Yet if quintessence exists, it's a very light boson that could give rise to forces that violate the equivalence principle. So experiments like STEP will be looking for exactly this type of thing. It's an example of a high-risk, high-payoff thing. Probably they will not see anything, yet if they do, it would truly change the way we think about the forces of nature.

Of course we're doing similar things here on earth. We're looking for new forces, and for new features of old forces. So we're doing experiments here on earth to look for violations of the equivalence principle, looking for different objects being accelerated by different amounts, in the gravitational fields of the sun or earth.

We're also looking for violations of the inverse square law of gravitational dynamics. When we talked about string theory in extra dimensions, we mentioned the possibility that some of these extra dimensions could be pretty big. They could be as large as a mm across. Right now we've been able to squeeze down the limit on the size of the extra dimensions, down to 1/10th a mm. We're going to continue to try and squeeze that down more and more.

This is again an example of an experiment for which if you find something, you absolutely win the Nobel Prize! You've found something incredibly important in the history of physics. The smart money bets they won't finds anything, but you don't know until you look, so we need to have some experiments that spend their time on the high risk projects.

Finally we'll emphasize the role of particle physics experiments in the future of cosmology. We've been talking about dark matter and dark energy, 95% of the universe. The evidence we have for dark matter and dark energy, comes from looking at the sky, by doing astrophysics, taking observations of galaxies and clusters, the CMB, the supernovae, and the whole universe all at once.

Yet ultimately, the explanation for dark matter and dark energy, will have to come from particle physics. The dark matter is some kind of particle, whether an axion, a supersymmetric particle, or something. The dark energy is even more mysterious, either quintessence, vacuum energy, or something even worse. To get a good idea of which of those models is more plausible than the others, we need to understand particle physics beyond the standard model. So doing lab experiments here on earth to increase our understanding of particle physics, is probably the single most promising way to learn more about the dark sector.

Right now we have the Tevatron at Fermilab just outside of Chicago, as the highest energy particle accelerator on earth, yet later in 2007, the LHC (Large hadron Collider) as CERN outside Geneva, will turn on. Starting in 2008, CERN and the LHC will be doing high-energy particle physics in a new realm we've never seen before. We're looking in exactly the regime where we should be able to find the Higgs boson, supersymmetric particles, and other particles just beyond the standard model. Not only are we looking for things that might very well be dark matter, and therefor 25% of the universe, but we'll also be hoping to learn things about sypersymmetry, extra dimensions, and other phenomena that come into the discussion when we talk about dark energy.

Now Sean admits the latter to be a very vague construction, not promising anything specific right there. Yet the point is that dark energy is so mysterious, we need all the help we can get. There's no known way that we can think of, to do a particle physics experiment to detect dark energy or see exactly what it is. Yet by learning more about the big picture, something that seems very unnatural to us, might suddenly make sense. So we're extremely hopeful that particle physics over the next five years, will be surprising us, teaching us new things about the fundamental nature of space, time, and matter, which ultimately will illuminate the nature of 95% of the universe we live in.

22. Beyond the Observable Universe - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture on the Multiverse is about as speculative as it gets. I remember Alex Filippenko sympathizing with the audience during his course's lecture on the subject, saying he knows this topic sounds way out there, but no one really understands it. Sean Carroll approaches it more seriously, perhaps less sympathetically, but more importantly he clearly lays out the various schools of thought.

Combining the two previous complex lectures sounds daunting. Inflation and string theory do not predict dark matter or dark energy, but there are important implications, especially for dark energy. The problem with the vacuum energy value seeming so non-natural leads us to try some king of recalibration. The Quintessence and gravity modifications seem like more natural values, but have experimental problems.

The compactification of the many dimensions of string theory leads to phase changes. But the Cosmological Constant problem creates 10E+500 of phases, or different possible vacuum energies.

The Anthropic Principle deals with the values that allow us to exist, whatever the definition of us may be. That leads to an environmental selection of values we can choose from. The tautology that the universe must have certain values for us to be able to be here observing it is balanced by the predictions we can make of the ensemble of the so many things we see.

Saying that our universe is homogeneous can sound very parochial from our limited point of view, or very parsimonious from our knowledge of the universe. We are limited in observing our universe by the CMB, so cannot be sure of either statement. We must allow for both to be true and make predictions. The Multiverse of string theory allows such sort of abstract experiments. The vacuum energy is just one of many parameters where the whole set of possibilities is called the landscape.

The curled up dimensions discussed earlier could unwind themselves into a small unique set of possibilities. Inflation has the flux of virtual particles where one patch could become dominated by dark energy and accelerate by inflation. Once again there are 10E+500 possible ways this could happen.

Sean carefully admits how this kind of talk can sound illegitimate and non-scientific. But considering such an ensemble with all its possibilities, natural and non-natural, may allow us to see if we ourselves are actually rare or common. Finding which versions of quantum theory or string theory values could work for various part of the multiverse is legitimate.

Within the ensemble there will be selection effects making some parts inhospitable for any observers to exist. But what are the observers? Are we defining them to our own bias? Consider a part of the multiverse where a heavier proton decays into a lighter neutron. This neutron world would be very different to us without chemistry or observers. But we can't know for sure that this is the case. Neutron molecules could form for all we know.

We should care about these scenarios after considering that the vacuum energy of our universe should be at the Planck scale, 10 to the 120 times larger in value than we observe today. Yet if it were that large, we would not be around to even consider it. Not even one proton would be able to exist. If it were 10 to the 120 times less in value than today, the universe would have collapsed long ago.

So if the vacuum energy is small enough for our existence, we either had to get lucky or we just happened to get lucky. The latter could be due to some dynamic mechanism making the vacuum energy low according to some physical law, or just due to the vacuum energy just being a random number. This randomness is possible, but unsatisfying. Sean gives an example for the former, were we just got lucky. A planet with an atmosphere that never allowed scientists to see the sky, has them trying to understand the temperature. They reason that there are just so many other planets out there, that some will have a nice temperature. Objectors say that sounds just too philosophical.

Think of that atmosphere as our CMB. The vacuum energy equals its value due to some equation or it's an environmental variable that is different from place to place. The latter is then a selection effect, not a law of physics.

Therefore we can try to make predictions about the ensemble. Steven Weinberg did such a thing in the 1980s by saying the Cosmological Constant should be roughly +/- 10 times the current matter density. We've now found that value to be 2 or 3 times, so he was right. Can we predict things like masses of particles or the amount of dark matter? More dark matter implies more structure in the universe to make galaxies. But Sean sees this as a stretch, more of a postdiction than a prediction. Environmental selection is also not a constraint, like the axion versus supersymmetric form of dark matter.

There is a divide between those who think the Multiverse can be used as a vacuum energy experiment, or that the whole idea is just plain crazy! The latter is then again divided into the grumpy old men objectors and the non-grumpy old men objectors.

Sean takes the former less seriously. They say the Multiverse is not scientific and no predictions are really recalibrating nature. Sean sees this an unconvincing and that science is possible. Look at how we dealt with the unnatural horizon and flatness problems by finding how inflation made them natural. The vacuum energy may make more sense in a Multiverse, that would lead to better understanding of the science.

Sean takes the non-grumpy objectors more seriously. Some say there will not be any important and detailed predictions that come from study of the Multiverse. Sean points out that the Steven Weinberg Nobel Prize might be used to refute this argument. But did he really just get lucky? Weinberg's Multiverse was the same as our universe in every respect except the vacuum energy. He derived his prediction of vacuum energy roughly equaling matter density, only from that difference.

But that is not what the Multiverse tells us to do. Everything changes from place to place, the dark energy, the perturbations, etc. So the Weinberg example was a less strong prediction. A true prediction would not be as precise as Weinberg's makes it seem to be. A typical observer in the infinite Multiverse would be nowhere near to such an answer. We need much better models of inflation or string theory, and if not, then we never will be able to make true predictions.

Imagine an infinite number of observers seeing X, while a greater number of infinite observers see Y. Is X or Y necessarily right? Back to earth, Sean agrees this is all extremely speculative, but it might turn out to be right.

The real lesson is that there is no convincing value of vacuum energy. That drives us to environmental selection and the Multiverse is the best we can think of right now. It could be the right answer.

The worst anthropic version we could think, is that the universe is arranged as we demand it to be. We should keep an open mind as our data lets us focus more and more on a correct version.

In this lecture we're going to get the payoff from the previous two, on inflation and string theory. Talking about string theory, we realized that we would like it to be the case, that namely what we think of as the unique string theory that lives in higher numbers of dimensions, predicts things like dark energy and dark matter composition. Yet this doesn't quite turn out to be true. String theory predicts too many things and as far as we can tell, it's compatible with all sorts of different possibilities.

Nevertheless it has an impact on how we think about dark matter, and especially about dark energy. So in this lecture we'll talk about how ideas from string theory and inflation, change our notion of what constitutes a natural vale for the vacuum energy. Remember that after we talked about dark energy existing, and going through all the different possibilities for what it might be, the possibilities of quintessence ad changing gravity were interesting yet ran into problems with experiments.

The possibility that it is vacuum energy, an absolutely constant amount of energy in every cm³ of space, didn't run into any problems with experiments, yet seemed very unnatural. The value the vacuum energy would have to have is just so very different from the value it seems to actually have in our universe. So string theory has the chance to recalibrate our notion of what it means for a number to be natural, and that is the long precess we'll go through in this lecture.

So the punchline is that string theory says there can be many different phases. All the different ways there are of taking the extra dimensions of string theory, and all the different branes and other things it predicts, and compactifying them down to get a four dimensional spacetime like the one in which we live, can correspond at low-energies to different phases of spacetime.

Just as water can come in different phases, liquid (water), solid (ice), and gas (water vapor), it's the same underlying thing. It's not like there are three different theories for each. It's the same stuff, manifesting itself in different forms. Likewise with string theory, it's saying there are perhaps 10 to the 500th power of different phases for spacetime. All these different ways in which the fundamental vibrational modes of the string can show up as particles, as numbers of particles, and as the vacuum energy.

The vacuum energy is going to be a number that changes from phase to phase, from compactification to compactification, so will take on all sorts of different values that total some 10 to the 500th power! Within that ensemble, we're going to get a lot of different possibilities, and one might just be the one in which we live.

This idea is sometimes called the anthropic principle. The idea that we're picking out, among a huge ensemble of possibilities, those which allow us to exist. The reason why that's a sticky situation is because we don't know what "us" means in that sentence. What kind of definition do we have for what counts as intelligent life?

So we're not going to go into any of those issues in any detail, but we'll rather think of it as environmental selection. It's not a surprise that if you live in a universe or set of universes in which conditions can be very different, that we're going to observe those conditions that are hospitable to us living there. That is just a tautology, and is not surprising.

The interesting part is when we go from the tautology to using it to make predictions. Within this ensemble, what is likely for us to observe? we might be able to change our notion of what you would expect ahead of time, by realizing we live in an ensemble of many possible universes, rather than in one unique thing.

So we live in a universe that we can't see in its entirety. The observable part is defined by a horizon. We send back light rays into the past, and because the speed of light is finite, those rays hit the boundary of the Big Bang at a finite distance. There's almost certainly parts of our universe which we can't see because they're simply too far away. That is not a surprising claim or controversial in any way. We can certainly see out to the CMB, and if we're trying to be clever about it and learn how to use neutrinos or something like that, we can push that back a little further. Yet there's still a very clear demarcation past which we can't possibly see, given to us by the Big Bang itself.

So what is beyond that part that we can see? The part we can see, seems to be homogeneous and isotropic. Not only is the configuration of stuff more or less the same, the same density of stuff from place to place, but it seems from our observations that the laws of physics are the same. It's not true that the charge of the electron is a different value in one part of the universe than any other. As far as we can tell, they're the same everywhere.

So is it possible that you can just extend that understanding infinitely far? Is it conceivable that we live in a universe where conditions really are the same everywhere, even outside what we see? The answer is absolutely yes. There's no reason we can give, either logically or within the laws of physics as we currently understand them, against the idea that the universe is truly the same everywhere, even for outside of what we observe. Yet by exactly the same criteria, there's no reason we can currently give to say the universe is the same everywhere. It is absolutely just as reasonable to say the universe is very different outside.

On the one hand you might say that it's very parochial, very anthropocentric of us to take out local universe and extend it all over the place. On the other hand you might say that it's not very parsimonious to have a universe that is wildly different. We have a universe which looks very nice as it is, why not just take the simplest possibility and extend it all over the place? The point is that we can't answer this question, just by pure thought.

So when we're in a situation like that, what we have to do is allow for both possibilities. We don't need to make a decision, but we're going to ask what happens if the different things are possibly true. So for this lecture we'll ask what happens if there are different regions of the universe, where conditions are very different?

So we're going to call this the multiverse, yet not in any metaphysical sense. It's not like there are different universes that are separate from each other by some profound difference. They're just different regions of space, into which we cannot get. That's an interesting thing to think about as a possibility, but it's string theory and inflation that takes this possibility and makes it very tangible.

In other words, string theory plus inflation gives us a set of ideas from which we can talk about the possibility of a multiverse in a scientific way. It is string theory that allows space to take on different conditions. Not just different densities, but different phases. So the different ways we have of taking the extra dimensions of space in string theory, and curling them up, give us different low-energy physics.

In our current world we seem to have four dimensions of spacetime, with three of them as large dimensions of space. We also have the standard model of particle physics, which is characterized by a set of particles and numbers. So we day we have certain fermions, bosons, interactions relating the particles, and parameters like charge, mass, and so forth. One of those parameters is the vacuum energy.

So when string theorists realized there was more than one way to compactify the extra dimensions, they saw there was going to be a huge number of ways. Something like 10 to the 500th power, is the current best guess. They've given the name "the landscape" to this set of possibilities. So the string theory landscape is something we can think of as like some jagged landscape here on earth, and every little minimum, every little local valley is a different place you can live. Different valleys of course are going to have different local conditions, temperatures, densities, heights, etc.

So that's an analogy to what we have in string theory, where there are different ways to curl up the extra dimensions. Yet perhaps not in an infinite number of ways, so perhaps it's not "anything goes." Yet that number of different ways is still very large, 1 followed by 500 zeroes in huge indeed.

Now we're very far from being certain that this is actually true or not. Currently our best understanding of string theory says there are perhaps 10 to the 500th power, different ways to curl-up the extra dimensions. However it's certainly conceivable the current state of the art just isn't good enough to say that for sure. In other words it's possible that once we understand string theory better, we'll come to understand that even though you can curl-up things in different ways, they don't stay curled-up like that. You might curl-up the extra dimensions in a certain configuration, but they quickly unwind into a different one.

It is therefor still quite possible that once we understand string theory better than we do today, we will narrow it down to a very small, perhaps even unique set of possibilities. That is a goal to keep in mind if it's true, but the current best-guess on the basis of what we seem to understand right now, is that these different phases of string theory really are stable and really can exist in principle.

So what inflation does is take phases of string theory that can exist in principle, and gives them a way to actually exist in practice. What inflation says is that at very early times in the history of the universe, we don't know exactly what was happening, but perhaps there were chaotic fluctuations. Different conditions were going on all over the place, there were very high temperatures, very large fluctuations from place to place.

In some tiny little patch of that initially chaotic system, you got a domination by something like dark energy. Some inflaton field with an approximately constant ρ, which caused that little patch to accelerate, to expand to a huge size. Eventually the energy within the inflaton reheated into matter and radiation, so we see what we see today.

So if you take the idea of inflation and combine it with the theory of 10 to the 500th power different possible stable final states for the compactified dimensions of string theory, you get a way to make those possibilities real. By starting inflation in slightly different conditions, by allowing inflation to go on in slightly different ways, you can have different trajectories, all of which populate anyone of the 10 to the 500 different valleys in the landscape.

In other words, we're imagining a multiverse that starts out in some chaotic condition, and then through inflation happening in different parts, different, ways, using different physics, we get a final condition in which you get huge bubbles of universe, all of which could be in any one of the 10 to the 500 different phases of string theory.

Clearly there are a lot of details to be filled in when we talk about something like that. Right now there's a lot of hand waving involved, and we don't know the correct picture. Yet that kind of picture is perfectly plausible. It might very well be, according to what we understand right now, that the universe we observe is a tiny infinitesimal fraction of everything there is. It is arguable that this is the lesson of Copernicus. If you're not putting us at the center of the universe, you shouldn't assume that the conditions we observe, are the same that obtain all over the universe.

So one thing we'll talk about is whether or not this is legitimate or OK to talk about regions of the universe which we cannot see? People will say that if you can't observe these different regions of the universe, they have no affect on local physics, no affect on what is going on in our region of the universe, and they never will, therefor talking about them isn't even science. So who cares about whether or not they're there?

Well the reason why we'd possible care, and we'll talk about this in more detail later, is because living in our ensemble changes our notion of what is natural. If you only live in a unique universe, then you might guess that the constants of nature will naturally take on the values that would seem easy to us if everything was of order one, if there were no large differences between the different numbers that you saw. Yet if you live in an ensemble, then every possibility happens, even some extremely rare ones.

If one of these extremely rare possibilities is somehow more hospitable for us to live in there, then we should not be surprised if we live in one of the rare possibilities. It would be very natural for us to live in a universe in which the parameters of nature, somehow didn't seem natural. That's why it's worth thinking about this possibility that we live in an ensemble, a multiverse of different phases of string theory.

Other people will say in a related way that it's not a scientific theory if it doesn't make scientific predictions. We should point out that the multiverse is not strictly speaking, a theory. The multiverse if it's there, is a prediction of a theory, the theory of strong theory combined with inflation. Now that's not a very exact theory right now. We don't understand either inflation nor string theory, well enough to tell us precisely what the predictions are. Yet the goal of this kind of way of thinking, is the following.

Someday we'll be able to do experiments that will convince us that a certain theory of quantum gravity is correct. Hopefully we'll be able to narrow down on the basis of data, on the basis of experiments, which version of string theory or quantum gravity, if any, correctly describes our world. We will within those experimental constraints, be able to say that the following fields can act like inflatons, so can make the universe expand.

In other words on the basis of data, we will build a framework that makes a specific prediction for what the multiverse should be like. Within that prediction, you can begin to make sense of questions like what should people observe who live in that ensemble? So even though the prediction of the multiverse is itself not testable, it might be an airtight prediction of a model that had other testable predictions. That may or may not be a Utopian goal, but that is the kind of thing we are shooting for when we think about these ideas in the back of our head.

OK, so now the philosophy is a little bit out of the way, so lets try to talk about putting this to work. What if we really do live in a multiverse. What if there really is an ensemble of different places that we don't observe where conditions are very different? Well it goes without saying that within that ensemble of different possibilities, there will be very strong selection effects when you ask what is observed by a typical member of that ensemble?

We imagine, roughly speaking, that some of these places in the multiverse are very inhospitable. We just can't live there. So it is not surprising that no one is observing them, if observers cannot exist. Now we admit that there's a very big question here of what is an observer? What is somehow what people call a conscious person, or some intelligent scientist who can live, if the laws of physics are very different? You could ask very detailed questions about this.

For example, imagine a universe that is almost exactly like our own, yet in which the proton was a little bit heavier than the neutron. We talked about this when discussing the standard model of particle physics. What would happen is, a proton would then decay into a neutron, since heavier particles decay into light ones. So instead of a world made of atoms, where you had atomic nuclei surrounded by electrons, you have a world made of neutrons. It should be clear that such a world would be very different from a world in which we live. You can't have chemistry in a world made of neutrons.

You might therefor ask, can such a world have intelligent observers? Some people think they know the answer to that question, yet Sean does not think that he knows the answer! He could hypothetically perceive that neutrons could get together, making little nuclei made of 1, 2, or 3 neutrons. Then these nuclei could even get together to make neutron molecules which could build up into neutron amino acids. He truly doesn't know whether or not there is sufficient room for complexity in a universe made almost all of neutrons, to support intelligent life.

Therefor he doesn't care, and he won't talk about any predictions we could make at a very quantitative level, that say if we increase the mass of the proton by 10%, then life cannot exist. We're going to keep an open mind about that, and stick to things which we think every reasonable person would agree on, do say something about whether conscious observers can exist.

In particular, we're going to talk about the vacuum energy! This is one thing we think has a very unnatural value. If it is the dark energy, the vacuum energy is 10 to the -120 times what we thought would have been its natural value. That seems preposterously finely tuned from the point of view of ordinary particle physics. If everything were natural in the standard model, the vacuum energy would be at the Planck scale, at 10 to the 120 times bigger than it is today.

However, nobody Sean has ever met, claims that life could exist if the vacuum energy were that big. If it were that large and positive, the acceleration of space would make it absolutely impossible to form planets, or for that matter, individual atoms! You couldn't even make a proton in the universe where the vacuum energy was the Plank scale, and everything would be ripped apart very quickly. You'd be left with an empty universe almost instantaneously, so there's no room to form life in such a universe.

If the vacuum energy had the magnitude of the Planck scale and were negative, it would make the universe re-collapse in one Planck time, much too small of a timescale to have any realistic or interesting particle physics, and much less to actually form life. In other words, when it comes to the cosmological constant, we have a very strange situation. The cosmological constant is just a different word for the vacuum energy, and it should be at the Planck scale, so that's its natural value. Yet if it had its natural value, we would not be here to talk about it!

So on the one hand, it's not surprising at all that the cosmological constant doesn't have its natural value. It can't have its natural value, or we wouldn't be here thinking about it. The question is why do we live in a universe in which the vacuum energy, the cosmological constant, is small enough to allow us to be here?

There are basically two different possibilities. One is that we just got lucky. In other words, there is no reason why the vacuum energy is small enough to allow for the existence of life. It just happened to be that value. Within that possibility of the "just got lucky" idea, there are two sub-possibilities. One says we truly just got lucky, so it's not only that the vacuum energy is small, but it's just a random number. There's no dynamical, physical explanation for why it's small, it was just randomly chosen and happily turned out 10 to the -120 what it should have been, therefor we can exist.

That is an absolutely possible theory of the value of the cosmological constant. Sean can't tell us that theory is wrong, but for obvious reasons it's kind of unsatisfying. It would be a truly lucky roll of the dice for us, for the vacuum energy to be that small. The other possibility within the idea that we just got lucky, is that there is a dynamical mechanism. The thing that we got lucky about is not that the cosmological constant is a random number that is small, but that the cosmological constant is small because there is some physics that we haven't yet figured out that makes it small. We're lucky for the existence of that physics, not for the random throw of the dice that made the vacuum energy very small. Yet right now, we don't know what that physics is. We're just guessing at it. Many people are hopeful that we'll find it at some point, but we just don't know.

The other possibility within that "we just got lucky" that the cosmological constant is small, is that we had to get lucky in the sense that the cosmological constant is not a once and for all constant of nature. It's an environmental variable that takes different values from different places. If the cosmological constant takes different values in different regions of the multiverse and in some of those regions it's small enough that life can exist, then it's not a surprise. Then it's not that we got lucky that we exist in those regions.

Let's get an example. Imagine that an analogy of astronomers who lived on a planet, where the atmosphere was opaque and could never see the sky. On this planet the temperature was very mild and never changed. It was 70 degrees everyday, but you couldn't see anything besides the clouds overhead. In such a universe, in such a hypothetical situation, what would the scientists who live on that planet try to do? They would try to understand the temperature that was on their planet. They would ask if there were laws of physics that predicted the temperature would always be 70, and we could be here?

Well other physicists on that planet would say, "my idea is that there are also other planets, and the temperature is very different there." Yet there are just so many planets, that life is going to arise on those planets where the temperature is nice. Others will say, Oh come on, that's just philosophy not science, we can;t see these planets so how can you be talking about that?"

Our current situation is actually much like that. Just like there are clouds in the sky of this hypothetical planet, we have a horizon given by the CMB, past which we can't see! Maybe there are other regions of the universe out there, where conditions are very different. The fundamental question before us now is, if the vacuum energy is a once and for all constant of nature, for which there should be some equation that predicts its value, or is it an environmental variable? Is it different from place to place, and therefor chosen by a selection effect, rather than a deep law of physics?

So if we're going to decide between those possibilities, it would be nice to take this idea that there really is an ensemble of different possibilities, and actually use it to make some sort of predictions. So not just to use it to make us feel good about the value of the vacuum energy, but to actually do something precise with it. We'll want to consider the entire ensemble and ask what a typical observer living in that ensemble of multiverse, actually observe?

So this very exercise was undertaken in the 1980s, by Steven Weinberg, a well-known physicist who won the Nobel Prize for his work on the standard model of particle physics with the W and Z bosons. Well he says that we can actually attach numbers to this statement, that if the cosmological constant were large and positive, it would rip things apart. It it were large and negative, it would make the universe re-collapse. He did a little calculation and argued that the typical value of the vacuum energy that would be observed by a conscious observer, was something like 10 times as big as the matter density.

He means that the vacuum energy could be anywhere from -10 times the matter density, to +10 times the matter density. So you pick a random number between -10 and +10. A typical number would between these would not be 10 to the -5 power! It's going to be on the order of 1, like +3, -5, or something like that.

So in 1988, Weinberg made this prediction that someday we'd observe a non-zero cosmological constant. This was a prediction he made before we went out and found it. So then 10 years later, we did find it, and in fact it was consistent with his prediction. The vacuum energy we think we have observed, is 2 or 3 times the matter density. That is consistent with being between -10 and +10. Not only is it between there, but it's kind of a typical number you'd expect it to be if you picked a random number between -10 and +10.

So what does that mean? It means that you can predict something, or at least you can try. So you might want to try and predict other things, such as the masses of the elementary particles, the mass of the electrons, the quarks, and so forth. Even better, you'd like to predict something we haven't yet observed, to make sure we're still on the right track. The problem is the environmental selection that says we can only exist where conditions allow for us to exist, isn't a very strong constraint on things we haven't yet observed.

What is the dark matter? Is it a WIMP, is it the LSP, or is it the axion? The environmental selection principle doesn't tell us which one. We can exist just as well, with both axionic dark matter or supersymmetric dark matter. You could even ask how much dark matter should there be? Some brave souls have tried to argue that the environmental selection principle, predicts that there should be dark matter. The reason why is because the more dark matter you have, the more structure you form in the universe, the more galaxies, and therefor the more observers. To Sean personally, this seems like a bit of a stretch. It seems more like a postdiction than a prediction. We already know that is dark matter there, we're trying to justify it after the fact.

Yet he thinks that for vacuum energy, there is some possibility of something going on there. We don't know exactly what will go on, we don't yet know how to predict things we haven't observed, but it's still interesting to try and push our current knowledge of how the ensemble would work, past what we get.

Nevertheless, let's give equal time to the objections to this way of thinking. We should say that currently within the physics community, there is a sharp divide. There is a set of people who take very seriously the idea of the multiverse as an explanation for the observed vacuum energy, and an equal number or larger, who think it to e completely crazy! So we'll give the arguments from people who think that even talking about this is not what we should be doing.

There's two basic kinds of objections to talk about the multiverse. One is what we'll call the grumpy old man objections, and the other are what we'll call the sensible objections. The former are the ones that just say, "Doing stuff like this isn't science, as you could never observe the stuff out there, so you're giving up on our attempts to understand the universe based on evidence, observations, and experiment!"

These are un-convinving to Sean as reason to not think about the multiverse. First, because it might be like that. It might be the case that outside what we can observe, the universe takes on very different conditions. Whether or not we can observe them, it might be the truth, and ultimately our goal is to get at the truth, by what ever method we can. If the way we get there is by naturalness arguments, rather than direct experiment, then that's what we have to live with.

The second is that the multiverse is not, as we said, a theory that makes strong predictions. It's a prediction of a theory that we can use to recalibrate our notions of naturalness. The point is that when we look at naturalness, when we look at quantities we measure in nature and say, "That one doesn't look right, it looks unusual to us," we're taking that as a clue. We're saying that we really don't understand the final laws of physics, but we're trying.

Sometimes the way we're moving toward the final laws is to do an experiment that gives us more information. Yet other times, the way that we move toward a better understanding of the final laws of physics, is to look at unnatural features of our current understanding. For example, that's what happened with the horizon and flatness problem in inflation. We thought there was a good understanding of how the early universe behaved, but w didn't know why. Thinking about the reasons why the universe would be nearly flat and homogeneous, led us to inflation. Thinking about the value of the vacuum energy, might very well make more sense in the context of a multiverse, that might lead to a better understanding of other things.

The non-grumpy objections Sean takes more seriously. There's a set of objections to thinking about the multiverse that we think are quite reasonable, and we should take seriously. So basically what these objections are saying is that even if, in principle, we do live in a multiverse with various things going on, as a matter of practice it is impossible to extract from that any detailed predictions.

Against this, you could say, "Well, Steven Weinberg who won the Nobel Prize, made a detailed prediction, what about that?" Yet there's a good objection to the fact that Weinberg made a prediction and sort of got lucky. The point is that he made a very specific calculation that did the following things. He said what if we had an ensemble of the multiverse, in which conditions in all the different parts were exactly the same as they are here, except for the cosmological constant? He only allowed the vacuum energy to change, and he derived the prediction of the vacuum energy that could be pretty close to the matter density.

Yet that's not what the actual multiverse situation tells us to do. It says that from place to place, everything changes. Not just the vacuum energy, but the set of particles we have, the way that inflation works, and so forth. If you are allowed to change not only the value of the vacuum energy, but other quantities like the value of the dark energy, or the amplitude of the initial density perturbations, you would make a much less strong prediction. The true multiverse prediction for the value of the cosmological constant, is not nearly as precise as Weinberg's calculation makes it seem to be.

So the truth is, we just don't understand the multiverse well enough right now, to make detailed predictions using it. What we're doing is saying that there's this set of universes, this set of places in the universe where conditions are different. There could be an infinite number of such places, and an infinite number of observers in every one of those places. We're trying to say, "What does a typical observer in that ensemble actually observe?"

The state of the art is right now, nowhere near being able to answer that question. It may be because we don't understand inflation and string theory very well, or it may be because we never will! That there isn't any right answer to this question. If there are a infinite number of observers who observe this, and an even larger infinite number who observe something else, how are we possibly to say which is more likely for us to be there?

So this is all speculation at this point in time. Yet the reason why it's worth going over is that it's speculation that might turn out to be right. The real lesson is that we don't have any convincing theory of the vacuum energy, and we're driven to the environmental selection in the multiverse as the best we can think of right now. It might turn out to be right, the worst version of the anthropic principle would be to think that the universe arranges itself into the way that you think it should be. What we should do is keep an open mind about all the possibilities as we get more and more data to help us zoom in on which one is ultimately correct.

21. Strings and Extra Dimensions - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

We've seen how Maxwell's EM theory and Newton's mechanics were unified in Einstein's special relativity. Then how special relativity and Newton's gravity were unified by general relativity. So now we are trying to unite general relativity and quantum mechanics (the standard model) into quantum gravity. But general relativity is a classical field theory based on energy and momentum where we can still pinpoint the location and momentum simultaneously. Quantum mechanics is a quantum field theory where energy and momentum are not fundamental but are broken down into parts by probabilities. The union would be a quantized spacetime, a quantum theory of gravity.

We need a cookbook to go from the classical to the quantum theory. Schwinger and Feynman's QED describes electron/photon interactions, the best example of classical theory that has been quantized. Newton's gravity when quantized does predict gravitons, but only in weak fields. EM theory when quantized predicts photons, but again breaks down in strong fields. Conceptual problems exist with quantum fluctuations and quantum spacetime. The latter turns into a big problem when time is considered. The technical problems are the infinities produced when equations are changed. QED works because it avoids them, but most others currently do not. Fermi's bosons initially produced infinities, but as more was learned they were able to be deleted. Quantum gravity currently does produce infinities, but string theory shows hope of finite, well behaved answers.

String Theory started out to explain the strong force of quark/gluon interactions. The connected lines of Feynman diagrams were replaced by paths of strings through spacetime. There was even a smaller number of simpler possibilities. It readily predicted a massless boson, with spin=2, coupled to energy and momentum; the graviton. Many other particles of the standard model were produced, but it remains very hard to connect string theory to our universe.

String Theory predicts ten dimensions while we only have three of space and one of time. There are ways to compact these dimensions down into a more reasonable number of six, such as the Kaluza Klein theory of curled up dimensions at low energy. The compacted extra dimensions even implies the three families we see in the standard model. Supersymmetry is even predicted but some are problematic such as axions, neutrinos with mass, etc.

It gets even worse with mem"branes." In our 3D world we can visualize 0D particles, 1D strings, and 2D branes. String theory is unique in that it cannot avoid to derives certain things, but it is non-unique in that it's 10D can be broken down into a large combinations of branes, strings, and particles that have just too many different ways to curl up the extra dimensions, ten to the 500th power!

But there turn out to actually be testable features. Earlier string theories had dimensions wrapped up in curls too small to be seen. But with branes there is a large extra dimension that cannot confine the graviton. It influences the curvature of spacetime with a gravity field in all dimensions. We see Newtonian gravity fall off at the inverse square of distance, because our 3D universe has area that changes as the rate of distance squared. But if we lived on a brane with 4D, gravity would vary as the cube, or 5D as the fourth power, etc. So tests are underway to verify how gravity varies at scales of 1 to 1/10 mm.

Strings are the size of the Planck Length, 10E-33 cm. Compare a proton at 10E-13 cm, twenty orders of magnitude larger!

Dark matter and dark energy taken together are about 95% of the stuff in the universe. However, they represent much less than the 95% of the lectures you can buy from The Teaching Company! So part of our goal in this set of lectures is to readdress that goal, to really concentrate on that 95%, on the dark matter and dark energy.

When we talked in the last lecture about inflationary cosmology, it's not because inflation gave us directly a theory of dark matter and dark energy, rather it relates to the background set of assumptions that we deal with, when we start talking about things like dark matter and dark energy. As cosmologists trying to understand the current universe, the idea that it probably underwent inflation at very early times, colors how we think about everything else. When we discover new things about the universe, it also colors how we think about inflation.

For the obvious example, when we discovered dark energy, it helped show that the prediction of inflation, that the universe was spatially flat, was something that was going to be correct. Likewise, the physics of inflation, with a scalar field that is slowly rolling and changing its ρ, only very slowly, has shown up once again in ideas for dark energy.

So today we'll be talking about a different background theory, that of string theory. A lot of people have this theory in the back of their minds when thinking about the fundamental laws of physics. That includes both particle physics as we know it in the standard model and perhaps beyond, and also gravitational physics as understood in General Relativity. Like inflation, string theory is a speculation, not something we know is absolutely true, but is something that has caught on as a very popular speculation. There's a tremendous amount of intellectual effort going on right now, trying to relate the ideas of string theory to the things we observe her in nature.

So the idea behind string theory is really extremely simple. It's just the statement that you replace elementary particles with elementary strings. In other words, in the conventional way of looking at things, if you take an electron, quark, or photon, and zoom in on it with the most powerful microscope one can imagine, they still remain point-like. They don't have any extent in any direction, and are just a fundamental geometric point.

String theory says that's not right. Instead, these particles are actually little loops of string. That is to say, they have one dimension of extent that takes the shape of a circle, and that circle is vibrating just a little bit. We don't know what the strings are made of, and it's not even a sensible question to ask. They're made of the stuff that strings are made of!

Yet the idea is that the different ways you can vibrate a string, correspond to all the different particles that we see. This theory has caught on for many reasons, primarily since it's a promising theory of quantum gravity, as we'll discuss. Yet also it's prospectively a TOE (Theory of Everything), including dark matter and dark energy. So we'll be talking about the possible ways that the ideas behind string theory can influence our conception of dark matter and dark energy.

As far as dark matter is concerned, there are sadly more than one possibilities for the way string theory can give us a candidate dark matter particle. It's consistent with our ideas of supersymmetry and WIMPs, as well as with out ideas of perhaps axions and neutrinos.

For dark energy, it's a trickier situation. You can get quintessence out of string theory, yet it's not very natural. The very intriguing suggestion is that string theory can offer an explanation for the size of the vacuum energy, that's the good news. The bad news is the explanation involves 10 to the 500th powers of spacetime which we don't see. So we'll evaluate that suggestion very critically in the next lecture, while in this one we'll try to set up what string theory is, why we're so motivated about it, and what the current state of the art is in trying to connect it to other things about the world.

So the reason why we care about string theory, is mostly because it's a prospective theory of quantized gravity. One theme we've had all throughout these lectures is that in physics, all the theories and data we have, have to be tied together. You don't have a separate theory for every phenomenon. You have the smallest possible set of theories that can explain the greatest possible set of phenomena.

In particular, you know that if your theories are going to be right simultaneously, they need to be consistent with each other. If you have two ideas that work really well in their respective domains of validity, yet are fundamentally incompatible with each other, then you know that something has to give. You know that either one of them is wrong, and needs to be replaced, or you need to find a third theory that takes both of them into account, and reduced to the two different examples and limits.

So this is a way that scientists can make progress, even in the absence of direct, explicit, and specific experimental data. Sometimes you know your theory is wrong, because you do an experiment and it contradicts the theory. That's an easy way to know that there's something which needs to be fixed about how you're thinking about things. Yet sometimes you know your theory is wrong, even though it's consistent with all the data you have.

That is a situation we find ourselves in right now. It's not the first time, since in the past this has worked. For example, in 1900 we had the theory of electromagnetism as put together by Maxwell with Maxwell's equations. We also had the theory of classical mechanics as put together by Isaac Newton. Yet these two theories were not quite compatible. They had different sets of symmetries and gave different answers to what would happen if you observed the same set of phenomena in two different reference frames.

So just by thinking how to reconcile these two points of view, Einstein was able to come up with the Special Theory of Relativity. Almost immediately afterward, he realized that this new theory was incompatible with Newton's theory of gravity, so that he would once again have to reconcile these two things. There was some experimental guidance, such as his being aware of the anomalous orbit of Mercury. Yet nevertheless his, primary goal was to find a single framework that could reduce in the right circumstances, both to Newtonian gravity and to Special Relativity, so he ended up inventing General Relativity.

So now we have a giant, looming incompatibility in the fundamental laws of physics. As far as we know, every experiment we've ever done, here on earth at least, can be explained by one of two theories. The General Theory of Relativity, Einstein's theory of curved spacetime as gravity, or the standard model of particle physics, a set of fields and their interactions governed overall by the rules of quantum mechanics and quantum field theory.

The problem is General Relativity is not a quantum field theory, but is a classical field theory. Even though in some sense, General Relativity replaced the ideas we got from Newton, in philosophy General Relativity is still very Newtonian! It says there is a state of the universe, there are equations that govern the evolution of that state, and we can observe that state in anyway we like, in principle to arbitrary precision.

The rules of quantum mechanics say something very different. These rules say we can't observe everything about a system. There is a wave function that tells us what the system is really like, yet when we observe it, we don't observe that wave function directly. There are certain observable features of it, and when we look at something, the observable thing we get, depends on the amplitude of the wave function. So that wave function is really telling us the probability for getting certain results when we actually observe something.

So we want to reconcile these two theories. It can't be the case that General Relativity is correct, and quantum mechanics is correct. If General Relativity is correct, then the source of gravity is energy and momentum, yet quantum mechanics is telling us that those are just things we observe, rather than the fundamental things that really are.

In other words, we could imagine, at least hypothetically, a quantum mechanical situation in which you had a gravitating body and its wave function said there's a 50% chance that it's over here, and a 50% chance that it's over there. Now try to ask the question, according to classical General Relativity, "In what direction does the gravitational field point?" "Does it point towards there or the other way?"

The hopefully obvious answer should be that there's a 50% amplitude that points there, and a 50% amplitude that it points there. That means that spacetime itself needs to be quantized. You'd have a wave function of the whole universe, of the dynamical properties, the curvature of spacetime itself. That is what we seek in a quantum theory of gravity, and we don't have it right now.

It turns out of course, that we have a set of cookbook procedures for taking a classical theory and quantizing it. The real world we think, is quantum mechanical. It's not really classical and then quantum mechanics is something we just add on top! The world is really quantum mechanical, and classical mechanics, a la newton, is something that is a limit or approximation to the true quantum mechanical reality that works very well when objects are really big.

When working with individual atoms or electrons, quantum mechanics is absolutely necessary. Yet when you're working with big objects, like the earth, the sun, or even us, classical mechanics is perfectly fine. So there's no reason ahead of time, that the way to find the correct quantum mechanical theory of reality, starts by taking a classical theory and then quantizing it.

Yet nevertheless it turns out to work awfully well in many different circumstances. The most successful theory that we have within the realm of quantum field theory, is QED (Quantum Electrodynamics). This is what won Nobel Prizes for people like Julian Schwinger and Richard Feynman. It is the quantum theory of electrons interacting with photons, and works extremely well. Yet we have a classical theory of electromagnetism that also works extremely well. The way to get quantum electrodynamics is to quantize classical electrodynamics.

When you try to take that cookbook and apply it to General Relativity, it works at first, and then it breaks down. So it's not as if we don't understand anything at all about quantum gravity. We can take the first few steps. For example you can consider gravitational fields that are weak, and spacetime that is almost flat everywhere, yet with tiny ripples on top of it.

In fact, most of the observable universe has gravitational fields that are pretty weak, so this is a very good approximation to many circumstances. We can quantize weak gravitational fields very easily. We get a theory of gravitons, a theory of particles that are quantized excitations of the gravitational field, in exactly the same way that we quantize electromagnetism and get a theory of photons, the quantized excitations of the electromagnetic field.

So the theory of gravitons works pretty well. It makes sense and we can scatter gravitons off of each other. Yet then we try to push this theory a little bit harder and ask what happens when the fields aren't weak, or what happens at very small distances? This is where is breaks down, and we have two kind of problems, technical and conceptual.

The conceptual problems are that if you have a background spacetime on which there are fluctuations in the gravitational field, you can quantize those fluctuations and the background spacetime is still more or less classical. Yet if you want to truly quantize spacetime itself, there become questions of, "What are we doing?"

In ordinary quantum mechanics for example, the wave function depends on time. You tell us what time it is, and we solve Shrodinger's equation to tell you what the wave function is. Yet now in General Relativity, time isn't out there and absolute. It's not a background in which we move, but it's part of spacetime, part of the thing we're quantizing itself! So should the wave function depend of time? It's more likely that somehow time emerges out of the correct understanding of quantum gravity. Yet even though we can say all those words, we don't know how it actually works. This is one of the things we're trying to address, one of the obstacles we have right now in making quantum gravity into a sensible theory.

Yet even without those conceptual problems, we have technical problems. That is to say, we try to think we know what to do, and we run into nonsense. There's a famous thing that often happens with attempts to quantize field theories, which is you get infinitely big answers. You can take two particles and scatter them, and ask according to the rules of quantum field theory, how likely is it that these particles actually hit each other and bump off?

If your field theory is well-behaved, like quantum electrodynamics is, you get a finite answer. There might be steps along the way in which it looks infinite, but at the end of the say, you get a very well-behaved, finite thing. For some theories, that doesn't happen, and your first approximation to the answer makes perfect sense, but your second approximation is infinity. Things break down and there's no known way to fix them.

Usually in nature when this happens, these infinities are a sign that new physics is kicking in that you don't understand. For example, Enrico Fermi's original theory of the weak interactions had this property. The first approximation worked well, yet the second was infinite, which was a problem. Yet now that we understand W and Z bosons, and understand the correct theory of the weak interaction, that problem has gone away.

So this problem exists with gravity, that when you scatter two gravitons off of each other and look closely at what the answer is supposed to be, it looks infinite. We therefor suspect that there's new physics kicking in, the equivalent of W and Z bosons, but for gravity. That is the kind of thing that string theory purports to offer us. The new physics that makes everything suddenly make sense and gives us finite answers.

String theory is just the idea that everything is made of incredibly tiny, loops of string! If you were able to zoom in with a superpowerful microscope, on what was going on at very small length scales, you'd be able to resolve individual things you thought were particles, into vibrating loops of string.

The reason you're not able to do that, is because the loops of string are ultra extremely small, approximately the size of the Planck length, invented by German physicist Max Planck to explain the scale at which quantum gravity begins to become important. In numbers, it's about 10 to the -33 power cm across. That sounds like a very small number, and indeed it is. We can compare it to the size of a proton, about 10 to the -13 cm across, made of three quarks and held together by gluons. So strings are very small, smaller than an atom by quite a factor.

In other words, the Planck scale is 20 orders of magnitude smaller than a proton. That's a much tinier length than any of our current particle accelerators are giving us access to. So if you look at these tiny vibrating loops of string, you will see them as particles. They look particle-like to us, because we can't resolve the fact that they're little one-dimensional loops of string. So when we talk about what string theory predicts, we'll still be talking as if it predicts different kinds of particles. There will still be photons that are particles, etc. Yet they will really be different vibrational modes of the string.

That is the idea behind how string theory is able to give rise to all sorts of different kinds of particles. It's not that the stringy stuff is made of different kinds of stuff for different kinds of particles. There is just one essence of string stuff that is the same for everything. Yet the little loop of string can vibrate in different ways, and these different modes of vibration correspond to bosons, fermions, what have you.

Interestingly there aren't that many ways to start with the vibrating string and get a consistent theory. In fact, since the 1980s when string theory first became really popular, it was thought there were five possible ways to start with a little loop of vibrating string and get one consistent theory.

These days, as we'll talk about briefly, we think there's only one way to do it. It's not that we've said the other ways are inconsistent, but we've found that what we thought were five different string theories, are actually just 5 different versions of the same underlying theory called M theory.

So this is part of the charm of string theory, that you start with an incredibly simple idea. There's just a loop of stuff and you quantize it. How simple could that be? There's really nothing else there. We're not leaving out any hidden assumptions. You find a unique theory somehow, you find particle physics, gravity, everything you want to find, just out of that little loop of string.

So in actually connecting it to the world, we try to make predictions. We try to ask how we relate string theory to particle physics? Well the first thing of course, is gravity. The reason why string theory was invented in the first place was as a theory of the strong interactions. In the late 1960s and early 70s, we didn't yet have QCD (Quantum Chromodynamics), which is the correct theory of quarks with different colors, held together by gluons. So we were still in the late 1960s, just guessing at what the theories of the strong interactions.

One person noticed that if you look at all the different particles that seemed to be relevant to the strong interactions, they arranged themselves with their masses and spins, as if they were little vibrating loops of string. String theory was born as an attempt to explain the strong interactions. Yet it didn't work, one reason being that it kept predicting a massless, spin=2, boson, that coupled to every form of energy and momentum.

In other words, string theory kept predicting a graviton, and therefor a theory of gravity. So even though you didn't want gravity, it still kept appearing in a kind of a miraculous way Ordinarily when we try to quantize gravity, we run into trouble such as infinities, conceptual problems, or whatever. Yet string theory is an example of a model in which you didn't want gravity. You were trying to explain how protons hang together, and yet you kept predicting gravity.

It turns out that not only do you predict a quantum theory of gravity, but it's a well behaved theory. One way of thinking about why you get these infinite answers in ordinary attempts to quantize gravity, is because the Feynman diagrams become exceptionally complicated. They describe the ways different particles can come together and interact, yet to a particle physicist, each one gets attached to a number. You can get complicated loops inside the Feynman diagram, and as those become small, the number attached to the diagram can become very large, possibly infinite.

What happens in string theory is that you replace Feynman diagrams which are just lines connected to each other, with the paths of strings through spacetime. So they look like two-dimensional sheets. You have a one-dimensional string moving through time, which describes a two-dimensional sheet moving through spacetime, which could describe a single particle splitting into two, for example.

The number of possible diagrams you can draw, describing such strings, is first of all, much smaller than the number of Feynman diagrams you can draw, and secondly, they are much simpler. It turns out that what string theory does is to smooth off the sharp corners that would be there in the Feynman diagrams of ordinary quantum gravity, and you begin to get finite answers.

Even better yet, you get more than a theory of quantum gravity. You can possibly get a TOE (Theory of Everything). The different ways strings can vibrate, give rise to gravitons. Yet also to photons, gluons, electrons, quarks, all the kinds of particles we know about in the standard model, can be reproduced by vibrating strings. That's the good news.

The bad news is that to actually reproduce them specifically, turns out to be very hard. It turns out to be very difficult to go from what we think of as "the unique theory of string theory," to the world in which we live. That's not really surprising, because in one sense gravity is really weak. Quantum gravity is something that is very far away from our experimental reach. We don't have a lot of explicit clues about how gravity and particle physics get together. We're left with only our IQ points, and sometimes they're good enough, sometimes they're not up to the job.

So what we're trying to do is take string theory, match it to the real world, so we can then ask what predictions string theory really make? The one prediction that string theory makes more than anything else, is that spacetime is 10-dimensional. Strings want to propagate in a space that is 9-dimensional, and then plus the 1 dimension of time.

The bad thing about that, is that it's not the real world. Yet at least the good thing is that at least it is the prediction of something. The question is if it is possible to reconcile 10-dimensional spacetime with the four dimensions that we see? The answer there is actually yes! It's been known for a long time, how to go from a higher dimensional space, to a lower dimensional space. If it had been the other way around, if string theory only worked in a 2-dimensional spacetime, we'd truly be in trouble. Yet it's easy to get rid of extra dimensions of spacetime.

String theory predicts there's six dimensions of space that we don't see. The way to get rid of them, is to curl them up. This is an idea that goes all the way back to Kaluza and Klein, soon after Einstein invented General Relativity. They said that if there are dimensions of spacetime that are dynamical and curved, maybe there are ones that we don't see, because they are curled up into tiny little circles or spheres. So string theory takes this idea and tries to take advantage of it.

It says maybe these extra dimensions that we don't see, really are there, yet are curled up into little balls the size of the Planck scale. That's the good news, and furthermore the different ways you can compactify those extra dimensions, tell us what the particle physics will look like at low energies. In other words, if string theory is right, the reason why, for example, we have three families of fermions in the standard model, turns out to be a particular topological fact about the space on which we've compactified the extra dimensions! We're turned a statement about the number of particles we see, into a geometrical statement about extra dimensions that we don't see.

That's interesting because it offers a new way to solve the kinds of problems we were stuck with, of why all these particles were there? The bad news is that there are too many ways to curl up the extra dimensions. The ways that we have to curl them up are not unique. From the mid-1980s when string theory first became popular, to the late 1990s, people were crossing their fingers and hoping that somehow there would be one way to compactify that was the best.

So people were trying to look for that, and found that with different compactification models, they could get all sorts of different possibilities. For example, supersymmetry is a robust prediction of string theory as well. That's good news for thinking about dark matter, because our favorite theory for thinking about what it might be is the LSP (Lightest Supersymmetric Particle).

Yet then it turns out that string theory also predicts the existence of axions, and that neutrinos should have mass. So so far, string theory is predicting too many things. It's not picking out one candidate for dark matter as the right one. Things got slightly worse in the 1990s when it was realized that string theory is not just a theory of strings. Remember that one of the virtues of string theory is that it's unique. You start at a particular place and derive things that are necessary, so you can't get around them.

The non-uniqueness comes from when you go from a large 10-dimensional world, and compactify it. There are many ways to do that, but in the original 10-dimensional description, things are very unique. So people realized that in that unique description, there lived not only 1-dimensional loops of string, but higher dimensional objects known as branes. This comes from the word membrane, which means a 2-dimensional thing. If you live in 3 spatial dimensions, the only things you can really easily imagine, are 0-dimensional particles, 1-dimensional strings, and 2-dimensional branes.

Yet if you have 10 dimensions, or 9-dimensional space to play with, then you can imagine 3 branes, 4 branes, 5 branes, that are 3-dimensional strings, 4-dimensional, 5-dimensional, etc. So it was discovered in the 1990s that all of these do play a role in string theory. There are different kinds of branes, some with miraculous properties, such as particles, strings, or fields, that are confined to the brane. In other words, you can have a brane living in some higher dimensional space, yet all the electrons and photons of this particular construction were stuck on the brane. They can't escape out into the extra dimensions.

So if you were made of those particles stuck on the brane, you wouldn't be able to tell that there were any extra dimensions. The interesting thing about this, is that is makes the problem on non-unique compactifications, even worse! Now not only do you have many non-geometrical waves to curl up the extra dimensions, but within those curled up extra dimensions, you can start putting in branes. You can start saying that maybe we live on some of those branes.

So we're faced now with a bit of a conundrum, stating from a set of unique ideas in 10 dimensions, we have a multiplicity of ways of getting down to four dimensions. The best estimates we have right now are something like 10 to the 500th power of possible ways to go from 10 dimensions down to 4, in ways that don't dissolve away too quickly. A potential place that you could imagine living in the universe of string theory.

That's the bad news, since we don't like it when we lose uniqueness somehow, and are still struggling to still find our way through those 10 to the 500 different possibilities. The good news though, is that some of those possibilities are experimentally testable. We don't know whether or not we're going to be lucky enough to be involved with one of the testable ones, but the point is that there are new ways that we realize for new dimensions of space to manifest themselves in experiments.

In the old days of Kaluza and Klein, when they first suggested that there are curled-up extra dimensions, all they did was just curl them up so small that you couldn't see them. We mean that no experiment which had been done by that time, could possibly reach them. Of course, since we haven't directly seen evidence for them, we still do the same thing today.

Yet now, when you have branes, a new possibility opens up. What if we really are living on some 3-dimensional brane, confined in some bigger space? Remember that when we say space is 3-dimensional, we do experiments that only perceive three dimensions. For example, if you take a stick, you can take a second one and tie them so they are perpendicular to each other. Then you can take a third stick and tie it so it's perpendicular to the first two. That means there are at least three dimensions of space, macroscopically. Yet try as you will, you cannot take a fourth stick and tie it there, so as to be perpendicular to all those other three at once. It can't be done, and is an experimental demonstration that we only have 3 dimensions of macroscopic space.

However, what if there are other dimensions, but we just can't get there? Then the problem becomes much harder. We could have large extra dimensions and just not noticed them yet. The real issue with this, is that even though we can confine the particles of the standard model of particle physics to a 3-dimensional brane, there's one particle you cannot confine, and that's the graviton. Remember that gravity is a feature of spacetime itself. Gravity is the curvature of spacetime. So if you have some object in a set of dimensions, it's going to have a gravitational field that stretches out into all the dimensions, not just on the brane.

How do we know how many dimensions gravity feels? Well we have Newton's law of gravity, the inverse square law that says two objects pull on each other with a force inversely proportional to the square of the distance. The reason why it's the square of the distance, and you can imagine the gravitational force lines coming from one object, is they fade away as 1/d², because the area they're covering goes up as the distance squared.

Yet that's only because we live in three spatial dimensions. If we lived in 4 spatial dimensions, the force between two particles due to gravity, would go like 1/d³. If it were 5 spatial dimensions, it would go like 1/(d to the 4th power), and so forth.

So if we lived on a brane, where the particles of the standard model were confined, but gravity leaked out, Newton's law of gravity still wouldn't be right. We wouldn't have an inverse square law, but would have an inverse cubed law, or fourth law, or something like that. So the clever suggestion was made in the late 1990s that maybe we do have an inverse cubed law, yet only on really tiny length scales. By really tiny we don't mean the size of a proton, but a millimeter across. So these are macroscopic length scales, where we had not yet done experiments.

So people started doing such experiments on these scales, testing Newton's inverse square law. They took a heavy plate and brought it very close to another heavy plate. They were able to squeeze the experimental limit on the size of extra dimensions, down from 1 millimeter, to 1/10th of a millimeter. That's a whole order of magnitude, which is a lot of progress, yet still it's very plausible to us today that there are extra dimensions of space a tenth of a millimeter across, and we just haven't noticed it yet.

So we need to push forward with this kind of idea. We can't get rid of the fact that there should be a quantum theory of gravity. We have quantum mechanics, we have gravity, we have to get them together. Especially as cosmologists, we care about things like where did the universe come from? Where did the fluctuations come from that we think are due to inflation? Our explanations for those fluctuations using inflation, said that you had quantum mechanical fluctuations in the early universe, during inflation, giving rise to density perturbations, of which we later measure their gravitational fields.

In other words, the inflationary scenario for explaining the observed density fluctuations in the universe, involves quantum gravity in an intimate way. If we want to claim to understand those things, we're going to need to understand quantum gravity.

What we really care about, of course, is dark matter and dark energy. So in the next lecture, we'll talk about how to take string theory, with all its extra dimensions and possibilities, and tease out implications for what the vacuum energy might be. There might also be implications for what the dark matter particle is, yet right now that's much more difficult to get.

When it comes to vacuum energy, string theory offers a very provocative, perhaps scary or even crazy, but at the very least interesting scenario, for why the vacuum energy of the universe might be the dark energy we observe.