12. Dark Stars and Black Holes - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This is the first of two lectures on speculations about dark matter composition, before we finally start talking about dark energy. Sean talks about the possibilities for ordinary matter making up the dark matter, while next lecture he will focus on the non-ordinary matter candidates.

It seems like much of the evidence for dark matter we have seen, already implies that it is non-ordinary matter. But since we have not yet found that non-ordinary matter, the theories for dark matter as ordinary continue to be numerous. This is the way science should be working properly. If you view Robert Hazen's Teaching Company course "Origins of Life" you will see this process in full action. Theories are being proposed all the time, the more surprising and testable the better, as Karl Popper said. Some of the most unorthodox are from the very leaders in the field. This is what makes science exciting to me. Sometimes we all need to take a step back and laugh at things. Primordial particle sized black holes? There has to be some right answer(s), so the imagination, creativity, and insight of these scientists are all on display for us.

The leading proposals are reviewed and each one is refuted on grounds of not adding up to enough mass compared to the amount of dark matter needed. It all points to the non-ordinary matter scenario of the next lecture. Supersymmetry theory proposes a natural way of making stable, massive, weakly interacting particles. Axions have similar qualities but are less plausible. Neutrinos are hot dark matter particles, so do not fit in with the leading theories.

We're almost halfway through the lectures, and we've learned an awful lot about the universe. Let's summarize what we've learned so far. We know first that the universe is big and getting bigger. By big, we mean that not only do we live in a galaxy with about 100 billion stars, but we live in a universe evenly distributed with such galaxies. A typical galaxy outside the Milky Way also has 100 billion stars. There may be 100 billion such galaxies in the observable universe, so it's certainly big by any standards.

It's also getting bigger,which means the galaxies are moving apart from each other. We can understand that in terms of Einstein's General Theory of Relativity. The space in between galaxies is itself expanding, pushing galaxies further apart from each other, and stretching the wavelength of light as it travels through empty space, giving rise to the cosmological redshift.

We also have a universe that is full of stuff, yet interestingly there is more stuff in the universe than what we see. We can weigh things in the universe. We can figure out how much mass they have, by using their gravitational fields. So we can take an individual galaxy and weigh it by looking at the motion of stuff outside the galaxy. We find that there continues to be more stuff in the galaxy, even when you can't see stuff anymore. Even when the visible parts of the galaxy stop, there's still more and more mass, as you go further and further out. This is evidence for dark matter.

This evidence is enhanced by looking at clusters of galaxies, at collections of galaxies moving around each other. You can look at both, how fast they're moving, to measure the total mass, you can look at the lensing of light that passes through the cluster, to measure the total mass, you can also look at the profile of x-ray gas in between the galaxies. Any one of these methods gives answers that are consistent with each other, and answers that the total amount of mass in the universe is something like 30% of the critical density you would need to have, to make the universe spatially flat.

So 30% of the critical density is a lot more than we can account for in terms of ordinary matter, in terms of the particles we know from the standard model of particle physics, that make up protons, neutrons, and electrons, the ordinary atoms that make up a table or ourselves. How do we know how much ordinary matter there is in the universe?

We've been emphasizing throughout the last several lectures that we have independent ways of measuring the total amount of ordinary matter in the universe. Two ways in particular are primordial nucleosynthesis, or Big Bang nucleosynthesis, the process by which when the universe was one minute old, it was converting protons and neutrons into helium and other light nuclei. The efficiency with which that happens, the percentage of helium you end up with at the end of the day, depends very much on how many protons and neutrons you have lying around. The more you have, the more helium by weight, you will end up with. So the fact that we have a certain amount of helium, about 24% of the visible mass in the universe, by weight, means that only 5% of the critical density of the universe can be made up by ordinary matter. That's not enough to account for all the mass we need.

Completely independently from that claim, we have the CMB. Slight variations in the temperature of the radiation that comes to us from when the universe first became transparent, 400,000 years after the Big Bang. These slight variations in temperature are all statistical, they are random fluctuations, but different sized regions evolve differently. Some will be enhanced in their temperature fluctuation by moving towards dark matter, some will be suppressed by pulling away from the dark matter, depending on how big that sized region is. So by looking at the distribution of different sized spots on the CMB, we can infer that there must be dark matter, pushing and pulling the ordinary matter we see. We get a consistent answer that's consistent with the claim that 5% is the density of ordinary matter, and 25% is dark matter.

There are other ways of getting similar results, ones that we haven't talked about. For example, you can start with the CMB and assume this is telling you about the primordial perturbations in density, and then let those perturbations evolve to today, to turn into galaxies and large scale structure. You can do this both with pencil and paper, and with a giant computer simulation. You find that in order to make as much structure as we observe on small scales, galaxy sized scales, it must be the case that there is dark matter in the universe, dark matter over and above the ordinary matter we can observe.

So many lines of evidence are pointing us to the conclusion that there's a lot of stuff in the universe that we don't observe directly, and that cannot be accounted for by ordinary atoms, ordinary things that are neutrons, protons, and electrons. We need some form of dark matter. Today's lecture gets down to the nitty gritty and talks about what that dark matter could possibly be. Now the answer that we think is right, is that the dark matter is some new kind of particle, not in the standard model of particle physics, yet is evidence for new physics that we haven't yet detected in the lab.

However, Sean wants us to trust him, and not think he's pulling something over on us, so today we'll consider carefully whether or not we might have made some mistake. Is it possible that the dark matter that we need to explain the motions of things in the universe, might somehow be in the form of stars or gas or dust, collapsed objects that we don't see because they're just too small, but are still made of ordinary stuff.

We're going to day at the end of the day that there's good reason to not believe this is true. Yet we want to go through the possibility, since some of the ordinary matter in the universe is in fact dark. Some of that 5% of the critical density, some of the protons and neutrons, we know we don't see. We don't see the air in the room, or different forms of gas and dust in the universe. In a cluster of galaxies, which we think is big enough to be a fair sample of the universe, we know that most of the ordinary matter is in between the galaxies. How do we know that? Because in the cluster, there's so much stuff that it falls together, heats up, and emits x-rays which you can observe. So you know that in a cluster, most of the ordinary matter is not in the galaxies, but 2/3 of it is in between.

We believe that clusters of galaxies are fair samples of the universe, by which we mean the ratio of stuff in between the galaxies and in the galaxies, should be the same, outside a cluster and inside a cluster. So we believe that even if you have stuff outside clusters of galaxies, which means most galaxies in the universe since most are by themselves, we believe it still should be the case that it's something like 2/3 of the ordinary matter in the universe that is not shining brightly in the form of stars in galaxies, but is in very dilute gas in between.

Yet nevertheless we think that even taking that into account, we don't have enough stuff to make up the dark matter in the universe. So today, we'll talk about different ways you can take ordinary matter and hide it in ways that are not very obvious. So in other words, we're going to talk about dark baryons! Stuff that started life as protons and neutrons, yet has come into a form that's not shining and easy to see, so is hidden from us somehow.

The simplest ways to do this, is to imagine that we have dark stars. A star that is a visible star, a bright star, starts life as a collection of gas and dust, spread across some wide region of the universe, yet is a little bit more dense than its neighboring regions. So just like a galaxy is formed when a whole bunch of stuff comes together under its mutual gravitational pull, stars are formed when stuff comes together under their mutual gravitational pull, in a much smaller region of space.

This same kind of process happens, but with stars, life is actually much more complicated. The process of star formation is one that astronomers don't claim to understand very well. It's a very active area of research in astrophysics right now, because somehow when this cloud of gas collapses, it heats up. Yet instead of bouncing back from the pressure force, it fragments into little tiny stars. Somehow this involves not only the gravitational dynamics of things collapsing, but things like magnetic fields, atomic physics, and the different ways that radiation travels through collapsing gas and dust. It's not a process we claim to understand, but what we can do is go out and look at the end results of that processes.

What are the kinds of stars that we actually see in the universe? The stars like the sun that we see, are easy to see because they're shining, they're giving off radiation. That's because they are so massive, that at the center, the hydrogen from which they are formed is being fused. Just like in the Big Bang, you're taking hydrogen, protons, hydrogen nuclei, and they're fusing together. When you take hydrogen, turn it into deuterium and then helium, you give off energy. The total mass of a helium nucleus is less than the sum of the masses of two protons and two neutrons. So it's able to give off energy by E=mc².

So the question is if there are things like stars, things that are collapsed collections of ordinary matter of gas and dust, and so forth, yet are not shining, maybe they are too small to shine, or something like that? Well yes there are things like that, and you want to ask how many of them are there, what forms do they take, and how do you get them? The simplest way is to start with an ordinary star. Start with a star that is burning its fuel and recognize that there's not an infinite amount of fuel to burn in that star. There's only a finite fuel supply, just like everywhere else. So a star will burn, like the sun for 4.5 billion years, which has another 5 billion years of fuel left, yet eventually will use it up. All that fuel will be turned into heavier elements.

If your star is low mass to begin with, the death of that star is fairly straightforward and calm. It just gives up, doesn't have enough nuclear fuel left, and in the latter stage it becomes big, a puffy red giant that gives off mass slowly into the outer reaches of space, while the core just slowly settles down into what we would call a white dwarf. This is a collection of gas that has been pulled together by its mutual gravity, yet has used up all of its nuclear fuel. So when it uses up its nuclear fuel, the reason why a star is so big in the first place, is because there is pressure created by the temperature that is created by that burning fuel.

The burning nuclear fusion process, heats up the interior of the star, and that's what keeps it big. When you've used up all the fuel, you don't have any pressure to keep it big anymore, and the star contracts. What is it that stops it from contracting? Well remember way back when we learned about bosons and fermions, we learned that fermions have the property that you can't pack them too tightly. The same reason that this table cannot collapse is because the electrons in the atoms are taking up space. The same thing will be true with a star. If it uses up its fuel and just collapses, eventually it will become the most efficient way to pack the electrons, protons, and neutrons, into a very dense substance.

That substance gives you a star called a white dwarf. It turns out that the electrons are the particles that take up the most space, so they define how big that white dwarf will be. It's the fermi pressure, named after Enrico Fermi of fermion fame, that keeps the white dwarf from shrinking any more. The laws of physics say that there's just nowhere to go. You can't put those electrons on top of each other.

If the star is slightly heavier than that, it will not end up as a white dwarf. It will burn heavier elements into yet heavier elements, in the way that a medium or low-mass star doesn't have access to. In that case, what will eventually happen after it puffs up and becomes a red giant, is that the core will violently collapse. Unlike a low-mass star that just sort of settles down, massive stars undergo a core-collapse, that goes very quickly to a small state, while its outer layers are blown off in a supernova explosion.

Now later in the course, we'll be talking in great detail about how to use supernovae explosions as standard candles to measure the acceleration of the universe. So right now Sean will let us in on a complication. These supernovae, are not those supernovae! There are different ways that stars can explode to become a supernova. This way that we're talking about now, is a core-collapse supernova known as a type II. Another way is what's called a type I supernova, which we'll talk about in later lectures as the ones that give us a standard candle that we use to measure the acceleration of the universe.

A core-collapse supernovae happens when a massive star has burned up its fuel, so the core shrinks and the outer layers are exploded off in what is a type II supernova. So what happens inside? We might have thought that things collapse and will form a white dwarf, since the electrons just can't be squeezed in anymore. This is true, yet there's something else that can happen if these particles have a lot of energy. We know that protons and electrons at these high energies can come together to form a neutron. So a neutron is a smaller particle than an electron. One of the miracles of quantum mechanics is that particles that are higher mass, take up less space. So that's why atoms have sizes that are controlled by their electrons, not by their protons and neutrons. It's the light particles that take up the most space.

So if you want to squeeze things together, but you're prevented from squeezing them because your electrons are taking up space, you do have an out. You have an equal number of protons as you have electrons, because your star is electrically neutral, so those protons can come together with the electrons and form neutrons. The neutrons take up less space, so if you turn off your electrons and protons into neutrons, you get a much more densely packed object, which we call a neutron star.

A neutron star is just a collection of particles that have all been turned into neutrons, and it is so dense that if you start with a several solar-mass star, you can turn it into a neutron star that is only tens of km across, the size of a city here on earth. It's very dense, and thus a high-gravity type of situation.

So you have two different possible end states for big stars. If a star is big, yet not too big, it will end up as a white dwarf. white because the surface is still pretty hot, so it gives off some light, but not very much. White dwarfs are actually very dim. If they are far away, you'd not be able to even see them, so they are candidates for "somewhat dark" matter! Neutron stars are very dim, are not giving off a lot of energy, so they could also be candidates for dark matter.

Finally, what if you had very low-mass stars? So low-mass they were almost closer to being planets than stars. We have in our solar system, gas giant planets, like Saturn and Jupiter. These are not stars because they are not heavy enough to burn nuclear fuel inside. You can imagine objects that come from the condensation of gas and dust, but weigh 100 times the mass of Jupiter. That is not heavy enough to turn on the nuclear fuel and start becoming a star. Such an object is called a brown dwarf, an object which is collapsed gas and dust, star-like in its initial stages, yet never hot enough to begin burning or shining.

So this means we have an entire collection of possibilities for ways to take ordinary matter and squeeze it down into some small, dense object, that doesn't give off a lot of light; a white dwarf, a brown dwarf, or a neutron star. So together, these are all candidates for a certain kind of dark matter. Yet their not the non-baryonic matter of dark matter, since all of these come from ordinary protons and neutrons, They started their lives as ordinary matter, they still count as ordinary matter in terms of nucleosynthesis or the CMB, but they're just ordinary matter hidden in a way that it's hard to find them.

So people have invented a clever nickname for these kind of compact objects; MACHOs (Massive Compact Halo Objects). So last lecture we had WIMPs, and this lecture we get MACHOs. This is not an accident! People have though about this for years. So MACHOs are a candidate for a way to take ordinary matter and hide it. To put it in a form that would be hard to see, and would look kind of like dark matter.

So we'll now give arguments that have nothing to do with Big Bang nucleosynthesis or the CMB, as to why MACHOs are not a huge part of that 25% of the universe we really think is not ordinary matter. Even if we didn't know from nucleosynthesis or the CMB, that the dark matter was not ordinary, could it be possible to rule out that possibility by ruling out these candidates, one after another? Sean would like to argue that yes, this is indeed the case.

So first, lets consider white dwarfs and neutron stars. White dwarfs and neutron stars are dim. If our galaxy were filled with many of them, they would act much like dark matter. They would be hard to see, they don't interact with each other, they don't run into each other that much, and they're very dense so that you can pack a lot of mass into these kinds of objects. The problem is we only have very specific channels for creating white dwarfs and neutrons stars. First, you have to make a big star, one that shines and eventually gives off its nuclear fuel to condense into a white dwarf or neutron star.

In the process of condensation, these stars give off a lot of mass, so it's a minority of the original mass of the star, that ends up in the form of a white dwarf or a neutron star. Most of the original mass of the star, gets ejected into interstellar space. So if you're trying to imagine that the universe is full of white dwarfs and neutron stars, then you're imagining that there's all of this stuff having been ejected into interstellar space, during the process of forming these white dwarfs and neutron stars.

That ejected mass just isn't there. We would be able to see it because it would have heavy elements in it, and be observed in the spectra of different objects. Yet it's just not observed. So in other words, there's no way to efficiently take ordinary matter and convert any substantial fraction of it into white dwarfs and neutron stars. There's no way that we know of.

For brown dwarfs, it's a little bit more complicated. The brown dwarf is not something you get by the end of a star, but something you create at the beginning as a very low-mass star. So how do we know there are not a lot of brown dwarfs in the universe? Well there could be, yet our most reasonable extrapolations say there are not. We can figure out how many stars are made as a function of their mass. You can observe the stars we do see, and see how many "very massive" stars there are, how many "medium mass" stars there are, and how many "not so massive" stars there are. From this, we can extrapolate to how many brown dwarfs there probably are. It turns out that the most reasonable extrapolations we have, say that there shouldn't be that many brown dwarfs out there.

Now Sean is the first to admit that this is not an air-tight argument. We could certainly very well be surprised. After all, if the alternative is new laws of physics, we should be thinking very hard. So what we can do, is come up with an absolutely new way of constraining the number of MACHOs in the universe, regardless of how they were made. We want to go out there and look for condensed star-like objects, even without knowing where they could come from.

The way to do that is to use gravitational lensing. Just like we used before to weigh galaxies and clusters, we can look for these tiny star-like objects, using gravitational lensing. The good news about MACHOs that lets us look for them using lensing, is that they move. The amount of lensing due to one tiny little white dwarf, or brown dwarf, or neutron star, is very little. You would not be able to notice a big deflection of a background object. However, if we get an exact alignment, so that a white dwarf is right in between us and a background star, than it will focus the light a little bit, and that background star will appear a little bit brighter than without the lens. It's just like putting a magnifying glass up to the sun, which makes it look brighter if you're right there at the point where things are focused on you.

The problem there is, of course, how would you know if something were right in the middle of you? The good news there is that things move around. These star-like objects, these MACHOs, are moving through the halo of our galaxy, or in between our galaxy and other galaxies, so we can look at a whole bunch of background stars at once, and wait for these events of the MACHO going in front of the background star. The brightness of that background star will be seen to go up and then back down, doing so in very specific ways. It will go up and down in a perfectly symmetric way, and absolutely independent of what color you observe. Every wavelength of light coming from that star will be amplified and then go back down again, in precisely the same way.

So there are projects going on to search for these microlensing events, and they have indeed found them. We see such data from one of these projects, a light curve, the amount of light that is coming from a single background star. They observe literally millions of stars, waiting for a coincident brown dwarf, or white dwarf to go by. Here we see the light going up and down, perfectly symmetric. This is a wonderful candidate for a microlensing event.

The point is that you look at millions of stars, waiting for these microlensing events. You find that there are not nearly enough of them to account for what we need to be the dark matter of the universe. So it's not a matter that we don't know how to make them. If there were enough brown dwarfs, white dwarfs, or neutron stars, to be a substantial fraction of the dark matter, you would have seen them using microlensing, and you don't.

There is of course, another way to make very dense stuff in the universe, and that is a black hole. If you have white dwarfs as the end-points of medium mass stars, neutron stars as the end-points of more massive stars, you can then ask what happens if we squeeze those neutrons together even more? Within the standard model of particle physics, there really is no place to go when you squeeze those neutrons. However, it is nevertheless the case, that according to General Relativity, something will happen if you keep adding mass to neutron stars. It can't last forever.

We think that if just collapses into a singularity, with a gravitational field so strong that light itself cannot escape. This is what we call a black hole, the end point of gravitational collapse, where gravity is as strong as it can possibly be. There's nothing left after that. Now you'd think black holes would be hard to detect in the universe, since after all, they are black. Yet we've stressed again and again that there are ways to detect gravitational fields in the universe, even if the thing you are looking at that creates the field, is not directly visible.

So ordinary matter, spinning around a black hole, can either be directly visible, or it can give off light as it's spinning. If you have a small black hole, the endpoint of a massive star, stuff that is spiraling into the black hole will heat up, and give off x-rays. This is one of the primary targets for x-ray astronomy, to look at accretion disks, as they are called. These are disks of gas and dust, swirling around, into a black hole, giving off x-rays as they go.

There's another class of black holes called supermassive black holes, that are a million or ten million times the mass of the sun. They live at the center of galaxies and we can detect them because what happens is stars orbit them. So what you see are stars moving in an orbit, which we can actually detect and make movies of in their elliptical orbits, around nothing. They orbit around a region of space where there isn't anything. We know how far away these stars are, so we know how big their orbits are. We can then measure the mass, confined to a really tiny region. The only way you can put that much mass, over a million times the mass of the sun, into such a tiny region, is for it to be a black hole.

So there are stellar-sized black holes that exist, there are supermassive black holes that exist, so could either one of these be an important part of the dark matter? Well the answer again is probably not. For stellar-sized black holes, all of the arguments that we used for MACHOs, still apply. First we have no way of knowing how to make them. You could make them from stars, yet that would eject a lot of mass. Second, they would be MACHOs and thus lead to microlensing events. Yet we don't see enough of these microlensing events, from black holes or anything else, to be a substantial part of the dark matter.

Yet then we have supermassive black holes. Could the dark matter be "million solar mass" black holes? So almost as we say this, we realize no, probably not! Such "million solar mass" black holes are hard to hide. It's true that you couldn't see any one of them, but if one is moving through a collection of stars and it's not all by itself, it would cause a lot of disruption of the total dynamics of that system of stars.

So supermassive black holes sit at the centers of galaxies, yet they don't play a significant role in the overall mass of the galaxy. It may sound like ten million solar masses is indeed a lot of mass, but remember that the mass of a galaxy is something like a trillion solar masses. So even though supermassive black holes exist, they're a tiny fraction of the total mass of a galaxy. They're not an important part of the dark matter.

The remaining possibility for black holes, is that in fact we could have primordial black holes. We could make black holes not from stars collapsing, or from things collapsing at the centers of galaxies, yet some process in the very early universe, creates black holes that are very tiny. That is something that is actually completely plausible in terms of dark matter candidates. We have no way of ruling out the possibility that the dark matter is such tiny black holes. If they formed before Big Bang nucleosynthesis, they would not count towards their counting of ordinary matter in the universe.

However, once you make the dark matter these tiny black holes, it's practically indistinguishable from making the dark matter out of particles. They're individual little objects, not big stellar-sized things. We can't look for them using microlensing. So we're back once again to the possibility that the dark matter is particles. What we'll do in subsequent lectures is go through all the different possibilities of ways to make particles that would count as dark matter. So black holes are one possible candidate for such dark matter candidates that are basically particles. They are very tiny, little black holes.

It turns out that they are not among the most promising candidates. The reason is that we don't know how to make them. We have no theory of black hole production in the early universe that would predict a large density of tiny black holes today. The best candidate theories we have for the origin of the dark matter, are those where we have a natural way of making them. So it turns out that the absolutely best candidate that we have for making dark matter, is something called supersymmetry, a new particle physics theory that naturally gives rise to a set of particles that are stable, massive, and weakly interacting, which is exactly what we want the dark matter to be.

There are other candidates, like the black holes we mentioned, there is a particle called the axion, there's even neutrinos that are in the standard model. For neutrinos there's a good idea why we don't like them, they're hot dark matter. The other particles are cold dark matter, but they seem to be less plausible from a particle physics point of view than supersymmetry. However, we are keeping an open mind. We don't yet know what the dark matter is, and that's part of the excitement of the next ten years of cosmology. We'll be trying to point our fingers very specifically on where the dark matter comes from.

11. The Cosmic Microwave Background - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture concludes the focus on the early universe, the second of the two larger cycles so far. Alternating between observation and theory, we used our development of the standard model along with general relativity from the first cycle, to characterize the early universe and its relations to dark matter. The stages of how we got to know, and why we believe in our current theories were accomplished, as outlined in the first lecture. Further speculations on dark matter will round out this second cycle, to be followed by the third on dark energy.

The previous lecture concentrated on matter in the early universe. Yet Sean restated that the early universe was radiation dominated. The Friedmann equation predicts recombination after 380,000 years. This is an atomic physics term referring to the electron returning to the atom after ionization. In our case the electron is not actually returning, but combining with a nucleus for the first time. Like so many other cases, recombination is actually a misnomer.

Before recombination the photons interacted with the free electrons and ionized nuclei so much that the scatter made the universe opaque. At recombination the temperature dropped enough to allow electrons to combine with nuclei to form atoms. The radiation does not interact as readily with atoms, meaning no scattering took place and the universe became transparent. But this radiation is the cosmic microwave background (CMB) seen today at a temperature of 3K. This snapshot of the 380,000 year old universe was as hot as our sun's surface. The scale factor of 1/1000 implies a temperature of 3000K. From our perspective, expansion over time has stretched the CMB's peak wavelength to the microwave portion of the spectrum.

The whole story of the first theories and observations of the CMB is well told by Sean. But the modern counterpart gets a little fuzzy, literally and lecture wise. Compared to the detailed particle physics descriptions of just seconds after the big bang, our picture 380,000 years later of the CMB seems to almost be the opposite. We have no theory of what the CMB should look like. The image of the CMB is quite good, showing the expected variations in temperature. But what those variations represent can be hard to describe. We can only predict their appearance over several angular scales. Sean goes through them a bit fast and without graphical support, so I will do my best to help out here.

The CMB snapshot being only 380,000 years old implies that a large blob of ordinary matter, say 1,000,000 light years wide, would not have had nearly enough time to gravitationally collapse. A blob as large as the universe is old, 380,000 light years wide, would still not yet have the time to evolve. A blob this size would appear just greater than one degree wide on a CMB map showing the whole sky.

A much smaller blob, far less than one degree wide, would indeed have time enough to collapse. But then enough time also left over to rebound, to become less dense and to cool off! This sets up an interesting effect much like that of an oscillating sound wave. Overall, the blobs on this much smaller scale would produce a smooth CMB map.

A medium blob just less then one degree wide would be just right, in that it would collapse but then not have time to rebound. A blob on this scale would show up best as a temperature variation in the CMB. If this sounds crude and primitive, especially compared to the nucleosynthesis from last lecture, I agree. It reminds me of the collapsing solar nebulae story, mostly elegant words to hide our ignorance. It doesn't help any that the course guide is more confusing than the lecture either. I'm finding that to be true in general for this course.

I think the three examples of blobs are also trying to say that a detector has to be set to observe for only certain sizes or temperature variations in order to actually see the fluctuations. But the real fascinating theory is how dark matter behaves with respect to the blob scenarios.

The dark matter initially collapses along with the blobs of ordinary matter. But the decrease in volume that serves to increase interactions and heat up the ordinary matter, does not happen to the non-interacting dark matter. So while ordinary matter rebounds, the dark matter continues to collapse.

At various stages the two are in and out of phase with each other, actually producing more temperature variations in the CMB. Supposedly we can see this effect to the degree that it implies a factor of five times more matter is needed than ordinary matter. This agreement with the dark matter implications from galaxy cluster dynamics, galaxy rotation curves, and primordial nucleosynthesis from last lecture, is of course very reassuring. Though Sean states it would actually be somewhat nice if the CMB result did not agree with the others, showing there was something new we didn't understand!

The grand conclusions are twofold. The critical density we so far had been setting equal to one as part of our own measure, is really equal to one according to the CMB. This implies there really is more than just ordinary and dark matter in the universe; what we now call dark energy.

The CMB also allow tests of our more advanced theories on the early universe such as inflation and polarization. The big bang is the poor mans particle accelerator, or so they say.

In the last lecture, we began our paleontological exercises, starting with looking at fossils from the Big Bang, leftover particles from the earliest moments of the universe's history, both using them to check that our theories of it are on the right track, yet also to put constraints on the stuff that makes up the universe, and to learn about our universe today.

Big Bang nucleosynthesis gave us a very nice way of measuring the total amount of ordinary matter in the universe, total amount of atoms, of stuff made mostly of protons, neutrons, and electrons. The answer is there's not enough stuff there to account for all the matter we perceive in the universe, so there must be dark matter that is the something else.

Today we're going to look at an even more basic relic of the Big Bang, which is photons. In particular the CMB, the background radiation left over from when the universe was about 400,000 years old. We may have already heard of the CMB in the context of providing evidence for the Big Bang theory. When the CMB was first discovered in 1965, as we'll talk about, it was still plausible to believe that the Big Bang wasn't right. There was an alternative called the steady state cosmology, in which the universe had been expanding forever, with more matter continually being created in empty space. There was not some hot, dense, original state, out of which everything came. Yet the Big Bang model made a very specific prediction, that there should be a leftover, very cold radiation, from that initial hot state. That's what this leftover radiation is today, the CMB.

Also, the CMB is important, because it provides static for our tv sets. If you have a non-cable tv, about 10% of the static that you see on your screen, is actually from photons coming from the cosmos in the form of the CMB. We only figured that out, after we'd discovered it by other methods.

Today we'll not really be so interested in the existence of the CMB, not really in its use for testing the Big Bang theory, but to look at the tiny variations in the temperature of the CMB from place to place. The very early universe is smooth, and the earlier you go, the smoother it is. So we talked about Big Bang nucleosynthesis and treated the universe as exactly the same everywhere. The CMB is the first time when the slight ripples in the universe, the slight perturbations in density, make an appearance. The effect is that things are a little bit different from place to place.

So the CMB provides us with a snapshot of what the perturbations in the early universe looked like, 400,000 years after the Big Bang. So by both looking at what they looked like then, and comparing to what they look like today, we can learn a tremendous amount about the constituents of the universe. Ultimately the CMB will provide us independent evidence, both for dark matter and for dark energy. Dark matter we'll talk about today, while dark energy we'll get to in a later lecture.

So the game we play by now should be familiar. We start with the universe now, and wind the movie backwards. We ask what happens when you take a volume of the universe today, and squeeze it like a piston, make everything more dense and squeezed into a smaller place, increasing along the way, the temperature. As the scale factor goes down, the temperature goes up, in exactly the inverse proportion.

So if the CMB we observe today is at about 3 degrees Kelvin, as a very cold set of radiation particles, when the universe was 1/1000th its current size it was at about 3000 degrees Kelvin. The reason why that's an important temperature is that it's when the photons were sufficiently hot, that when they were banging into atoms, they had enough energy to strip the electrons away from them.

In other words, at moments before the universe was 1/1000th its current size, there was too much hot radiation to allow atoms to exist. You had free electrons running around, unattached to atoms, and you had free protons and other atomic nuclei. They wanted to get together but they kept running into hot photons which prevented them from doing so.

So all this was happening, like we said, at about 400,000 years after the Big Bang. More specifically, 380,000 years after the Big Bang is the slightly more precise moment when it happened. We know all that from the Freidmann equation, the equation in General Relativity that relates the expansion rate of the universe, to the stuff inside.

So what the Friedmann equation is telling us, is that at earlier times than that, the universe was hot enough that everything was ionized, individual atoms were just a nucleus and the electrons were moving freely. That means that the universe was opaque. Remember that photons like to interact with charged particles. They can interact with atoms, as the photons cannot go through a table which is opaque, yet if atoms arrange themselves in the right way, photons will just go right through them. The air in a room has this property, where photons of visible wavelengths, travel right through it unimpeded.

However, when you're ionized, when you have free electrons going around, no photons can go through you unimpeded. Those photons will keep running into these free electrons, which will make them bounce and turn in a different direction. If you were alive during that era of the universe's history, which you couldn't be since it was far too hot, somewhat like living on the surface of the sun, yet if you put your hand up in front of your face, you couldn't see it. The photon couldn't make it from your hand to your eyeball, without bumping into a whole bunch of things. It was as if the universe was immersed in a thick, soupy fog, so you couldn't see anything.

There were a lot of photons. There's a rule of physics that says when something is hot, it gives off a lot of radiation, called black-body radiation. It doesn't matter what color the thing is, or how its excited the different atoms or anything like that, but it's just that any lump of stuff at some fixed temperature will be giving off radiation all by itself. This is how you can see people in the dark with infrared goggles, as their body temperature is enough that they're giving off thermal radiation, blackbody radiation. It's the same reason why a heating element will be glowing red, since it's just giving off blackbody radiation.

So the early universe, we know had to be filled with radiation, because it was at a high temperature. It has a blackbody spectrum which we can actually test by observing the CMB today. So the moment of the universe becoming about 3000 degrees Kelvin, is when recombination happens, when electrons can finally get together with protons and other atomic nuclei, to form atoms.

Recombination is a word from atomic physics that is used when you take an electron off an atom, and it then goes back. So you've removed it, and now it is recombining. Sometimes people say you shouldn't use this in cosmology, since it's not recombining. It was the first time these things ever combined! That's being a little too tricky in fact, since in the real world, what happens, even in cosmology, is that a typical electron and proton will combine and recombine many times at that temperature of 3000 K, before they finally settle down.

Yet when they do settle down to form atoms out of the ions you used to have, the universe has now become transparent. You had a lot of radiation running around, you had blackbody radiation suffusing the universe, and now that radiation stretches freely throughout empty space. It can go through the gas of hydrogen and of course can go through the dark matter and neutrinos, they won't bother you!

So that photon now has a path that instead of being really short, can stretch for billions of light years. All that radiation was being created at every point in the universe. So we, living here right now, can look around and see that radiation coming at us, if nothing ever happened to it from the moment of recombination, 400,000 years after the Big Bang, until today when we bump into it. So the universe becomes transparent at about 3000 degrees Kelvin, which is actually pretty hot, similar to the surface of the sun. The sun is not emitting microwaves, but visible light, which is why we see it.

Yet of course, what happens is that the universe expands by a factor of 1000 in between recombination and today. So the light that was given off at recombination, was actually similar to what we see from the sun, yet gets redshifted, stretched in wavelength by the expansion of the universe. Today it has reached to the microwave regime. The wavelength of this stuff from the early universe is the same as what you use in a microwave oven to heat things up. It really is that kind of microwave.

So this entire story of the early universe emitting blackbody radiation, it being opaque when the universe was ionized, and then suddenly becoming transparent when recombination happens, was worked out in the late 1940s and early 50s by George Gamow and his students, Ralph Alpher and Robert Herman. We heard about Alpher and Gamow in a previous lecture. They also worked out Big Bang nucleosynthesis for the first time, and the prediction that there should be something called the CMB, was actually made by these physicists as a spinoff of their work on primordial nucleosynthesis.

So they are making these predictions by about 1950. They didn't have very good astronomical data, but were still ale to predict that the CMB should exist and should have a temperature of something like 5-10 degrees Kelvin, as their guess. It turns out to be more like 3 degrees K, but that's extremely good, considering the quality of data they had at the time.

Again however, they were ahead of their time. They made a prediction by about 1950, and no one had the technology to even go look for this stuff. It was very unclear to Gamow, Alpher, and Herman, when they were writing their papers, whether anyone would ever be able to even detect this CMB radiation they were predicting.

As it turns out, in 1965, Arno Penzias and Robert Wilson, working at Bell Labs, succeeded in detecting the cosmic microwave background. This was back in the day when Bell Labs, owned by Bell Telephone, would do basic research just because it was interesting! They were not trying to build anything better. Well, of course they were all trying to build better things, but they were investing in research because they just wanted to learn about the universe!

So radio-astronomy was a hot, new topic at the time, and Bell Labs was heavily invested in radio-astronomy. Penzias and Wilson were young radio-astronomers who had built new receivers and were trying to calibrate them into looking at different objects on the sky. They built a large, horn-shaped antenna, located in New Jersey, in Holmdale, and tried to bring it online for the first time.

Penzias and Wilson didn't know that there was any such thing predicted as the CMB. They were interested in looking at radio-astronomy sources, stars and nebulae which were inside our galaxy. Yet when they were trying to calibrate their new telescope to make sure it was working, they kept getting noise, some background buzzing that they couldn't get rid of. The reason they were puzzled was no matter which direction they pointed their telescope, they got the same kind of noise. To them this meant there was a problem with the telescope, not something they were seeing in the sky. If it doesn't matter where you look, it's probably because your instrument is faulty somehow.

Yet they went through every single check they could think of, trying to remove this noise from their instrument, and even climbed into the horn to scrape off the pigeon droppings from the inside of the instrument, because they were a dialectic material, giving off microwaves. Eventually they realized they couldn't get rid of the signal, and realized they were actually receiving microwaves from the sky.

First, purely by accident they were informed by a friend that there was a preexisting prediction for a CMB. Second, there was another group down the street at Princeton, New Jersey, who knew about this prediction and were trying to detect it. Bob Dickie, a physicist at Princeton, along with his graduate students Jim Peebles and David Wilkinson, knew about the CMB. Dickie had predicted it independently after Gamow, and they were engaged in an attempt to build a receiver to detect it. They were building something on the roof of the physics building at Princeton University, not knowing there was a much better telescope which was by accident, down the street discovering the same thing.

So at the end of 1965, Penzias and Wilson published a paper, while Peebles, Roll, Dickie, and Wilkinson published a theoretical paper explaining what Penzias and Wilson had seen. These two papers appeared side by side in the Astrophysical Journal. Penzias and Wilson's paper was entitled "A Measure of Excess Antenna Temperature." They didn't say out loud that what they had detected was in fact, the relic radiation from the Big Bang. They admitted in the paper that this was a very promising interpretation of it, but just like Hubble, years before, they were good observers, telling you what they saw in the universe, leaving it to us to interpret where it came from.

So Penzias and Wilson won the Nobel Prize for their work by 1978, yet nobody won any Nobel Prize for predicting the CMB! Alpher and Herman, who were still alive at the time, while Gamow has passed away, thought that they would win the Nobel Prize, since they had predicted this wonderful thing that was then observed. Yet they had predicted it so early, that everyone had forgot about it! Even though they kept trying to tell people, they never really got the recognition that most people now think they deserve, for doing both Big Bang nucleosynthesis and the CMB.

You do, by the way, feel bad for the poor photon, from the CMB. We're talking about a photon, which in the very early universe, kept scattering off of electrons. Then the universe became transparent and that photon traveled across tens of billions of light years, without bumping into anything, only to land in New Jersey, to be detected by some physicists. Yet it was for a good cause, because the CMB today is very useful to us, for doing astrophysics.

So the important thing when they were discovering the CMB, was that it was there, with a temperature to be measured. The CMB at that time, to the best observation anyone could make, was perfectly smooth. You look in every direction of the sky and you get the same temperature. Yet everyone knew that couldn't be strictly true. In our current universe, it's not perfectly smooth, yet more or less smooth in sufficiently large regions. So if you go back in time, it must have been pretty smooth, yet not perfectly so.

That meant that there must be fluctuations in the temperature of the CMB, which grew into the larger perturbations we see today. You could even figure out how large the fluctuations in temperature should be. They should be one part in 100,000. So if you see the CMB being at a certain temperature at one point, you go over to a point next to it, then it should be different by 1/100,000.

So that is where the action is today, in measuring the perturbations in temperature of the CMB, and using them to characterize the behavior of structure formation in the universe, and the ingredients that go into that structure as it forms. These tiny variations in temperature of the CMB were finally detected in 1992 by COBE (Cosmic Background Explorer), a NASA satellite. It was the second most complicated satellite NASA had ever built, after the Hubble Space Telescope.

So COBE just sat there, taking data. At the time when launched, there was a previously existing experimental result, which brought into question the fact that the CMB was really a blackbody. Some people had put up a telescope on a rocket, which measured a deviation in the blackbody spectrum. People were worried about that, so the very first thing COBE did was to verify that the spectrum of the CMB was indeed a blackbody. There was a talk at a AAS meeting that got a standing ovation, which rarely happens! The fact that COBE was able to verify the CMB as really a blackbody, was big news.

A year later, COBE went beyond that and found the tiny fluctuations in temperature from place to place in the CMB. A few more years later, by 2006, the boss of COBE as a whole, John Mather, and George Smoot, who was the boss of the specific instrument which found the temperature fluctuations, were awarded the Nobel Prize for doing that.

Since 1992, since COBE found that there really were fluctuations in the CMB, we have gotten much better at measuring these fluctuations. We've developed a large retinue of different ways to take pictures of the CMB. Here is an image of one such CMB experiment. This is the Boomerang experiment, which was launched on a balloon in Antarctica. The idea of a balloon is that you get above most of the atmosphere, so you have a clear view of the sky. The idea of Antarctica is that there are winds that go around the continent, so this is a very unusual kind of physics experiment, where you build it and then launch it in a balloon. The wind carries it off to the east, and you see it go that way. Then you wait two weeks and see your experiment coming back to you from the west! It has circumnavigated the continent once, so over the course of two weeks, you can collect that much data. Then you push a button, it falls down, and you collect your data in the experiment.

There were other similar experiments and telescopes observing the CMB in Chile, California, and at the south pole where we've gotten very good at measuring the CMB in different ways. Perhaps the best image we have of the CMB comes from MAP (Microwave Antisotropy Probe), renamed WMAP (Wilkinson Microwave Antisotropy Probe) after Dave Wilkinson, one of Bob Dickie's grad students in the early days, who became a pioneer and sort of the grandfather figure of CMB research. He was an important person on the WMAP satellite, yet passed away just before the first results were announced.

So we see an image of WMAP itself, a satellite which can observe the whole sky. That's the real difference between a satellite imager of the CMB, versus a balloon or ground-based imager. If you're sitting on the ground, or even in a balloon that is not very high above the ground, you can't see what is going on beneath you, behind the earth. A satellite can get a 360 degree view of everything that is happening in the CMB. What WMAP did was exactly that, and it returned this image, an iconic picture in cosmology, a map of the tiny temperature fluctuations in the CMB. The blue regions are a little bit cooler than average, the yellow and red are a little bit hotter than average. This is the snapshot of what the universe looked like about 400,000 years after the Big Bang.

So what do we learn from this? Where did this picture come from, and what is it telling us? The point is that we don't have any way, of predicting precisely where a cold spot will be, and a hot spot will be, on the CMB, anymore than we have any way of predicting where a galaxy will be in the sky. What we have are statistical theories, that predict we should get so many perturbations like this, so many like that.

So what you need to do is observe all of the CMB, and characterize the statistics of the different patches of hot spots and cold spots. That is something you can compare to a set of predictions. So how do you make that set of predictions? You're going to consider the life of a blob of stuff. So we imagine we have a little blob of stuff at very early times in the universe's history. A little blob that has a tiny bit more density than the surrounding plasma. So its wants to contract under the force of gravity, to get smaller and more dense.

Yet it may or may not succeed in doing that. What happens to this blob of stuff will depend on how big it is. Take a blob of stuff that will be, for example, lets say, at recombination, one million light years across. Well the age of the universe at recombination is only 400,000 years. So a blob of stuff that is a million light years across, doesn't have time to collapse.

So when we look at the CMB, it turns out that every angular size we're looking at, that is greater than one degree, corresponds to a physical size that is greater than 400,000 light years. So on scales greater than one degree across, when we look at the CMB, we're looking at things that did not have time to evolve. They are not telling us anything about the evolution of stuff in the universe, because they didn't have enough time to evolve themselves.

So let's look at stuff that was smaller than that. Let's look at blobs of stuff that did have time to evolve. What happens to them? So you have an over-dense region of the early universe with slightly more matter in it. So when it begins to evolve, it will contract. When stuff contracts, just like the universe or a piston or anything else, it heats up. So what initially happens is, the region of stuff which is slightly over-dense, contracts, heats up, and that forms a hot-spot you can observe on the CMB.

Yet you need to ask what will happen next? It's exactly like a sound wave, here in the room or anywhere else. There is a region of increased pressure, yet that pressure pushes things away, so things bounce back and become less dense than they were before. So you have a blob of stuff that contracts under its own gravity, it heats up and becomes hot, yet there's also more pressure that pushes against it and that same blob expands and becomes under-dense and cold. Once it becomes under-dense, it is surrounded by regions that are denser than it is, and the same process happens. The blob bounces back and forth. It's truly an acoustic wave, moving through the primordial plasma, just like a sound wave moves through this room. A moving region of high pressure, low pressure, back and forth.

So that would be interesting all by itself, yet there's more physics going on than just this oscillation. There are two important pieces of physics, one being that it doesn't oscillate forever. It is damped, just like when we say something into this room, you hear a slight echo, but you don't hear it forever. The sound waves bump into stuff and die away. These oscillations in the early universe will eventually damp out and stop because things are mixing, moving from dense regions to under-dense regions.

So if you look at very small regions, very small blobs of stuff, it is true that they oscillate, yet they damp out and stop. So for very small parts of the CMB, you don't see that much antisotropy. You don't see that much variation from direction to direction, or very much perturbation in the temperature of the CMB. On small scales, things have had time to smooth out.

On large scales, things have not had time to evolve from medium scales that are interesting. That's when things can collapse, heat up, then expand and cool down. Yet the other new piece of physics is of course, dark matter. The story we we're just telling of stuff collapsing and heating up, is one of ordinary matter. It's the story of atoms, of protons and electrons. When we say heat up, we mean stuff bumps into other stuff. It exchanges energy, and that's what causes it to heat up.

Yet dark matter is collisionless. Dark matter just collapses. Dark matter doesn't heat up. So in the first stages of this process of an over-dense region, it's a nice, very convenient feature of the universe, that if a region is over-dense in ordinary matter, it is also over-dense in dark matter. They go hand in hand.

So when things begin to collapse, both the dark matter and the ordinary matter collapse together in the same place. Yet the ordinary matter heats up, becomes high pressure, and then uncollapses, becoming less dense. Yet the dark matter just keeps collapsing, while the ordinary matter is oscillating back and forth. What you get is a series where the ordinary matter is in-phase with the dark matter, then out of phase with the dark matter, then in-phase, etc. Back and forth, the dark matter is either helping the ordinary matter collapse, or hindering it from expanding.

In other words, when we look at the CMB, at the pattern of splotches of hot and cold spots on the sky, certain sized splotches are being helped by the dark matter, and certain sized splotches are being hindered by the dark matter. You will get more variations in temperature at certain scales, than you will at other scales, if there is such a thing as dark matter.

So this was a theoretical prediction that's made very cleanly and crisply ahead of time. People knew what to look for, so when WMAP, other satellites, and experiments, were looking at pictures of the CMB, they were able to then do statistics on what kind of patches existed. How big the different splotches were, how much variation you had in temperature from place to place.

The answer is that you need about five times as much dark matter, as there is ordinary matter, in order to explain the pattern and temperature variations in the CMB. That number, five times as much dark matter as ordinary matter, should be familiar to us. That's the number that comes out of taking the total amount of dark matter that we infer from dynamics, and comparing it to the total amount of ordinary matter we infer from Big Bang nucleosynthesis.

In other words, completely independently, from either individual galaxies, galaxy clusters, or Big Bang nucleosynthesis, the CMB is telling us that we need non-baryonic dark matter. The patterns of hot and cold spots in the CMB, would by themselves be enough to imply that we need dark matter in the universe. Yet it is very good for the standard cosmological model, that this implication from the CMB, matches implications we had from other ways.

Of course it would be even better if it didn't match! That would mean that we're learning something new, that we don't understand what is going on, that it's a clue to something else, that we haven't yet figured out. Yet it's nice to have a theory that works. What the CMB is telling us, is that the theory of dark matter, plus ordinary matter, works. That a universe in which 5% of the critical density is in ordinary matter, 25% in dark matter, is one that fits not only galaxies, clusters, and Big Bang nucleosynthesis, but also the CMB.

So that is a lot of information we're able to extract from these patterns of hot spots and cold spots on the CMB. Yet we're not done yet! The CMB turns out to be a treasure trove of information, and we're going to get a lot out of it. It is certainly evidence for dark matter, and we'll show in a later lecture that it is also evidence for dark energy. The CMB implies very strongly that the total density of the universe, is equal to the critical density.

So far we've been using the critical density, the density of stuff that you would need to make the universe spatially flat. That's just a convenient way to measure how much stuff there could be in the universe. It might be that the actual density is only 30%. The CMB is telling us that this is not right, that the actual density of stuff in the universe is one, in units of the critical density. The actual density we have is critical, and the universe is spatially flat. So in other words, not only is there dark matter, more than ordinary matter, but there is also something else. There is also something besides the ordinary matter we see, and the dark matter we don't see, and that is going to be dark energy.

That's one thing we get from the CMB, and another one is testing our theories of the early universe. In a later lecture, we'll talk about inflation, which is our best candidate theory for where the initial fluctuations and density came from. Inflation is very much a speculation at this point in our history, we don't know whether it's right or wrong. Yet it makes some predictions like how things should appear in the CMB, that have turned out to be true. Yet we're still trying to do better. We want to know not only the temperature of the CMB in all directions, but how inflation makes predictions for the polarization that we see in the CMB.

So we are by no means finished observing the CMB. We are building new satellites, like the ESA (European Space Agency) satellite called PLANCK that will be launched in a few years, to measure the CMB to unprecedented precision. We're hoping that as we study this relic radiation from the Big Bang, with greater and greater instruments, with higher and higher accuracy, we will continue to learn more surprising things about the universe.

10. Primordial Nucleosynthesis - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture gets specific as promised, with a dense description of how our parameters of the early universe work to make the change into our current one. Sean admits this is a difficult lecture but the payoffs will be worth the effort.

Primordial nucleosynthesis is most confusing when presented as specific events at specific times. I prefer more general statements of trends, especially when just being introduced to the topic. Sean gives a good mix of both, but I will concentrate on the trends.

The freeze-out concept from last lecture is useful to understand how protons and neutrons can begin to survive as the universe expands, instead of being annihilated by anti-protons and anti-neutrons. The lighter protons are more abundant than the heavier neutrons, so their ratio is 7 to 1 (or 14 to 2). When 2 deuterium nuclei (1 proton, 1 neutron) fuse into one helium nucleus (2 neutrons and 2 protons), there are 12 protons remaining as free hydrogen nuclei. That ratio of 4/16 or 25% He to 12/16 or 75% H, is one of the great triumphs of cosmology. We can observe quasar light from the early universe and confirm this ratio.

This abundance of H, He, and other trace elements like Li, changes with the overall density of the universe. Our observations of these abundance ratios implies a density of 5% for ordinary matter. Thus another sign that dark matter is a new and different type of particle, since otherwise the abundances would have correlated so well.

The expansion rate and radiation are the key parameters of the early universe. As previously mentioned, the radiation of the early universe had not yet lost its tremendous energy that it quickly will, when the universe expands. If this radiation parameter is any different, such as another family of neutrino, it would greatly affect the Big Bang nucleosynthesis model. A different expansion rate would affect the production of helium, or imply a different gravitational constant, again affecting the model. It all fits together into a working unit.

The analogy from Sean is one of sinking a cross-court hook shot while blind folded. Yes, it is improbable that we have come to knowing these fundamentals about the universe. But I'm wary of these types of comparisons. The voyager slingshot assist from Jupiter is like sinking a pool shot from thousands of miles, using the cushion. The Hubble image is like seeing a dime in LA from NY. No real perspective is gained.

One can just as easily point out how much there is that we don't know. Ten years ago we didn't consider that the universe was accelerating or that 95% of it was of complete unknown composition. Ten years from now there could be another totally different focus in cosmology, the field is changing that fast. Maybe a lecture on Kuhn's paradigm shifts is in order? It will be interesting to see how the latter half of the course treats these issues.

In the last lecture we learned about how to go from the soup in the early universe, of particles and radiation bouncing into each other, to figure out what would be left over at late times. How to go from very high temperatures to very cold temperatures, like we have in our universe today.

In this lecture we'll give an example of this process, perhaps the most important example of which we actually have data about in the universe right now. That's the example of the light elements. We have the universe when it was one minute old, acting like a nuclear reactor, turning individual protons and neutrons into helium, lithium, deuterium, and other light elements. Today we can observe the amounts of helium, lithium, and deuterium, from the early universe. We can make predictions on the basis of our understanding of cosmology and particle physics, and test those predictions today, to see if we correctly understand what was going on in the very earliest moments of the universe's history.

So this is a fairly specific lecture. We're not going to talk about generalities anymore, but will dig into some very precise quantities. Yet it's worth the effort to follow what is going on, since the payoff is enormous. Compared to talking about dark matter and dark energy, it can seem kind of pedestrian to talk about nuclear physics, something that perhaps some 50 years ago was the sexy, hot topic, yet now we understand pretty well.

The point is that Big Bang nucleosynthesis, as it is called, gives us our best empirical handle on what was happening at the first moments of the universe's history. From that handle, we can infer things, not only about what was going on back then, but what is true right now. In particular, Big Bang nucleosynthesis provides us with a very believable and absolutely comprehensive measurement of the total amount of ordinary matter in our current universe.

This ordinary matter, from the standard model of particle physics, the actual mass density of that stuff, comes from protons and neutrons. In an atom, in a molecule of this table or in us, most of the mass and energy is in the atomic nuclei, in the protons and neutrons. Nucleosynthesis is intimately involved with how many protons and neutrons are laying around. For a different number of them, you would get a different prediction for helium and lithium and so forth. So the results of Big Bang nucleosynthesis tell us that the amount of ordinary matter in the universe is about 5% of the critical density, which is the density of stuff needed to make the universe spatially flat.

Now we don't know ahead of time that the actual, total density of the universe, is the critical density, but we can measure densities that we observe in terms of the critical density, and Big Bang nucleosynthesis says that protons and neutrons are about 5%. Yet we've already said that the total amount of matter in the universe, the amount of stuff that has accumulated in galaxies and clusters of galaxies, is something like 30%. That's why we know that not only is there dark matter, but that it's something new and different, not ordinary stuff, even as hidden as it maybe. So the goal of this lecture is really to present a convincing understanding of this chain of logic.

So we're going back to about one minute after the Big Bang. Again, we don't know what happens at the Big Bang itself, but using the Friedmann equation of cosmology, using our understanding of General Relativity, and how the curvature of space and the expansion of the universe responds to the energy density of the universe, we know what the temperature was about one minute after the Big Bang, or even one second afterward.

Back at that time, we had free protons and neutrons which couldn't join together to make atomic nuclei because the temperatures were too high. Yet as the universe cooled, the temperature lowerd enough so that a neutron and proton can now join and stick together.

Now if you had a bunch of neutrons and protons at a low temperature and you let them go to their lowest energy state, you let all the neutrons and protons transform into the state that they really wanted to be in, they would all be in the form of iron. This is the configuration of protons and neutrons that is the most stable. If you break apart an iron nucleus, the resulting particles will always have greater energy, no matter how much smaller than iron they are. Likewise if you take a heavier element than iron and break it down into iron, you will release energy, which is how nuclear reactors work. So you can either take much heavier elements and have them undergo fission, coming closer to iron, like uranium or plutonium, breaking into smaller nuclei, or you can have fusion where you have tiny little nuclei joining and thus going towards iron.

So if the universe lasted an infinite amount of time, and cooled off very gradually, it's easy to predict what the outcome of Big Bang nucleosynthesis would be. All of those protons and neutrons would turn into iron. The reason why that doesn't happen is because there's not enough time, since the universe is expanding quite rapidly. So one the one hand, the temperature is going down which allows nucleons to fuse into heavier nuclei, yet on the other hand the density is also going down which in turn lowers the frequency of fusion. So because they don't interact with each other, they can't fuse, and we don't go all the way to iron.

We're stuck with helium and all the other light elements. So lets run the movie backwards and start with our universe today, asking what would happen when the universe was smaller and things were closer together? It's extremely analogous to taking a bunch of stuff in a piston and just compressing it. That compression is very much like the shrinkage of the universe as you go backwards in time. So what happens is of course, things get pushed together and the density goes up. Yet as you push a piston in, the temperature of the stuff inside the piston goes up because things are banging together more frequently.

So the temperature and density of the universe goes up. That temperature is basically the average amount of kinetic energy of every particle, as we've said before. So the temperature of our current universe, which is the temperature of the relic photons of the CMB, is about 3 Kelvin. One degree Kelvin is equal to one degree Celsius, but the zero point of the scale has been moved, so that zero degrees Kelvin is the lowest possible temperature that exists. It's the temperature at which everything is absolutely zero, so it's called absolute zero, which corresponds to about -270 degrees Celsius.

So today, the universe is at about 3 degrees Kelvin and the earth is at about 300 degrees Kelvin, or something close to it. In other words, the universe is not in thermal equilibrium, and the temperature is different from place to place. So if we take this universe with the photons today being three degrees Kelvin, and we squeeze them as we go back in time, the temperature goes up, inversely to the squeezing. So when the universe was 1/1000th its current size, the temperature was about 3000 degrees Kelvin, which was when the CMB was formed.

When the size of the universe was a billionth of the size it is today, its temperature was about 3 billion degrees Kelvin, which is the era of Big Bang nucleosynthesis. We can also tell what times these correspond to, by using the Friedmann equation. It tells us that recombination, the moment when the CMB was formed, is about 380,000 years after the Big Bang. The time of nucleosynthesis is only at about one minute after the Big Bang, when the temperature was a billion times higher than today.

In that era, the matter was not dominated by matter and dark energy like it is today. Dark energy, as we'll talk about later, has an approximately constant density as the universe expands. Matter dilutes away in energy as the universe expands, because the density of particles goes down. Yet radiation has a density that goes down even faster, not only because the number of particles goes down, but also because the energy per particle goes down as particles get redshifted. So of the three kinds of energy, radiation goes away the fastest as the universe expands. Contrary wise, as the universe contracts into the past, the radiation goes up the fastest.

So even though today, radiation is a small part of the energy budget of the universe, at early times it was the dominant part. The early universe was radiation dominated, so that the things making up most of the energy budget of the universe were photons and neutrinos, light particles moving close to the speed of light.

So when the scale factor was about a billionth, the universe was very hot. The reason why that's an especially important time is that the universe was hot enough that individual atomic nuclei could not survive. The temperature of about 3000 Kelvin is the scale factor of about 1/1000th, when the temperature was too high for atoms to survive, so that electrons are torn from their atomic nuclei. Yet it's at 3 billion degrees K that individual nuclei cannot survive. So even if you had some atomic nucleus of oxygen, carbon, iron, or whatever, back then the temperature was so high that the protons and neutrons would just be torn apart.

So at times less than a minute after the Big Bang, at temperatures more than 30 billion K, you didn't have any atomic nuclei, just individual protons and neutrons. Before even then, you didn't have individual protons and neutrons, since the temperature was high enough to resolve them into their constituent quarks and gluons. Yet by one second or one minute after the Big Bang, you certainly did have protons and neutrons, and they kept bumping into each other.

We see a schematic picture of thermal history of the universe, as you go from the very earliest times when the temperatures were very high, a series of transitions occurs as the temperature goes down. The one we're talking about today, is the one where you make the light elements.

So lets start at about one second after the Big Bang. You have protons and neutrons going around, and one second is chosen because not only do you not have atomic nuclei, but one second is before the protons and neutrons have frozen out. Remember that freezing out is the moment when particles stop interacting with each other, the rate at which things happen dips down because the densities become too low.

At times earlier than one second, protons and neutrons were interacting with the surrounding plasma, which means they were being created and destroyed all the time. They were not in a total quark number 0 state, so there was more protons and neutrons at that time, than there were anti-protons and anti-neutrons, otherwise they would have all annihilated away.

There's some net baryon number laying around for reasons that we don't completely understand due to some unknown process of baryogenesis. Yet they're there and the forms that they want to take are protons and neutrons. So when we say they've not frozen out, we mean that protons and neutrons are converting into each other very rapidly.

So we talked about the process of a proton bumping into an electron and making a neutron and a neutrino. This can happen if the energies are high enough. So we're saying that when the universe was less than one second old, the energies were indeed high enough. Neutrons would interact with neutrinos to make protons and electrons. Then vice versa, protons and electrons would react with each other to make neutrons and neutrinos.

So everything was in equilibrium, which means you have more light particles than heavy, since they're harder to make. So the fact we know that the proton for example, is a little bit lighter than the neutron, when you can convert protons and neutrons back and forth rapidly, you'll end up with more protons than neutrons because the proton is lighter. It's easier to have it around.

So in fact, if you run the numbers, you plug in the equation, and find that at the moment the protons and neutrons do freeze out, when these weak interactions which are converting from protons to neutrons and back again, slow down so much that they don't happen anymore, that's a moment when you have about one neutron for every six protons. We can't derive that in real time, yet that's what comes out of the equations. You have about six protons and one neutron for every seven baryons lying around.

So then what happens? This is the time when you've frozen out, so protons and neutrons don't convert anymore. They just sit there! Yet of course the proton really does just sit there, and nothing happens to it. Yet the neutron isn't stable, since we know their decay rate is a half life (a 50/50 chance of decay) once every ten minutes.

Now we're talking about a timescale when the universe is only a few seconds old, so not many neutrons decay away. Yet between one second and one minute, some of the neutrons will decay away. Their lifetime is ten minutes so most will be around, but some will go away. So by the time we've reached a moment of about a minute after the Big Bang, we've gone from having one neutron for every six protons, to having one neutron for every seven protons. This is a number worth remembering since we'll put it to good use.

So we have one neutron lying around and about seven protons. The time is about one minute after the Big Bang and the temperature about 3 billion degrees Kelvin. What's so special about this time? The temperature is then low enough to start to form nuclei. Protons and neutrons can stick together without being continuously dissociated by bumping into other particles.

So it's worth pausing at this important moment in the universe's history, to emphasize that we're assuming a lot here. We weren't there at the Big Bang, or one minute after. We weren't looking at what was going on. So how do we know all these things we're saying? How do we know there was one neutron per seven protons, the temperature at one minute, etc?

The way we know is, we never know for sure, but we do have a theory. We have the Theory of General Relativity, we have the Friedmann equation for the expansion of the universe which was derived from General Relativity, and we use that theory, plus particle physics, plus the standard model, to make a prediction. We go from what we see today, to what the universe must have been like.

Yet we're not satisfied with making a prediction, so we're now going to test it. We'll say, "If the universe were doing that, certain things should be true today." So we're going to check it. Since those things will turn out in fact, to be true today, we're pretty confident that we understand what the universe was doing one second or one minute after the Big Bang.

So what happens? The temperatures now dip down low enough, that we can make nuclei out of protons and neutrons. So of course, you start with individual protons and neutrons, and you make the nuclei step by step. It's not going to happen that a whole bunch of protons and neutrons come together all at once, and make one heavy nucleus. Rather, particles will interact with each other one by one.

So the first thing that can happen is a neutron and a proton can come together to make a nucleus of what is called deuterium. This is heavy hydrogen, one neutron and one proton in an atomic nucleus. Now that's easy to describe, yet in fact a deuterium nucleus is very fragile. So this slows down what we might have thought would be the process of nucleosynthesis, since you can make a deuterium nucleus, but it's so fragile that they keep getting disrupted at this early time of high temperature in the universe's history.

Yet the temperature is dropping bit by bit, continually going down, so eventually two deuterium nuclei can last long enough to bump into each other, and they make a nucleus of helium. This has two protons and two neutrons, which is sticky and robust. It is not very fragile so once it's made, it stays there.

So basically we start with one neutron, and seven protons. Or if you like, we double the number, two neutrons and 14 protons. Basically every single neutron that you have lying around, goes into a nucleus of helium. So these two neutrons and 14 protons become one helium nucleus, and 12 protons.

The helium nucleus has four particles in it, two neutrons and two protons, and you have 12 protons lying around. So 25% of the mass that you started with, has now become helium. This 25% of the baryons, of the total number of protons and neutrons, are now stuck in a helium nucleus.

What you'd like to have happen next, if you could just stay at that temperature forever, is for those helium nuclei to then stick together. You would start making carbon and oxygen and heavier elements. Yet what actually happens is that the universe expands, so it doesn't happen. The helium just gets stuck there.

So realize that this statement which we make with such confidence, of course depends on details of what was going on, just three minutes after the Big Bang. It depends on the expansion rate of the universe, since if it were much slower, then you would have time to go from helium to heavier elements. In the model we're working with, in the Theory of General Relativity and the Friedmann equation, you end up with almost all helium, about 25% by mass.

You can do better than that. Beside the fact you get 25% helium, you get trace elements that contribute just a little bit. Not all of the deuterium is sucked up into helium, and there's some little bit left over. Not all of the helium nuclei stick around by themselves. Sometimes the helium nucleus will take on other little particles, and perhaps become a nucleus of lithium. Lithium-7 has three protons and four neutrons in it, another light element. You can also have helium-3, with two protons and one neutron.

So in other words, primordial nucleosynthesis takes individual protons and neutrons, and from that makes a whole bunch of helium, all the helium it can make, plus trace abundances of deuterium, helium-3, and lithium. In particular, it does not make anything heavier, like carbon, oxygen, iron, all the stuff that is very important for our lives. So when this theory was first being invented, it was in the late 1940s actually. The first paper on primordial nucleosynthesis was written in 1948 by George Gamow and Ralph Alpher. They were trying their best to make all the elements that we know, in the Big Bang. They were trying to make all the heavy elements, yet they eventually realized it doesn't quite work.

Yet they did realize they could make helium very efficiently, and that the observations in 1948 weren't very good. Yet the predictions that they made, fit very well that the observations that helium actually existed. This was the first quantitative thought that we could extrapolate our knowledge from the current universe, all the way back to moments after creation. So Alpher was actually a graduate student of Gamow's at the time, and this work was his Ph.D. thesis. It's defense was attended by 300 people from the Washington DC area, and the Washington Post had a front page story the next day, "Universe Created in Five Minutes."

Seans' Ph.D. thesis did not appear on any front page of the daily newspapers, but he imagines it to be a nice thing when that would happen! Yet Alpher was not always happy with how things turned out, since Gamow was quite a practical joker. So when they submitted their paper, by Alpher and Gamow, he added the name of Hans Bete into the middle, so that the author list read Alpher, Bete, and Gamow! It was a joke, supposed to sound like alpha, beta, and gamma, from the Greek alphabet. He didn't even tell Hans Bete, who is a famous nuclear physicist. He didn't even tell Ralph Alpher, was was the lead author on the paper. Alpher was upset since now he was going to lose some credit, with two very famous collaborators, not just one.

Nevertheless, we now have a theory of where the heavier elements came from, and know that they were not born in the Big Bang, but were born in stars. They are both created while stars burn, like our sun right now creating carbon and oxygen, and then they'll be scattered when the stars explode in supernovae, which will at the same time make even heavier elements. The very heavy elements of gold, plutonium, and uranium that we see in the universe, are created not in the centers of stars, but in the actual process of the explosion of a supernovae.

So to test Big Bang nucleosynthesis, we have a set of predictions. We have 25% helium roughly, trace amounts of deuterium, lithium, and helium-3. The problem is that the late universe is spoiled by all these supernovae explosions. There's more and more elements processed by stars, so the abundances we see today are not the primordial abundances. What we want to do then, is to take observations of pristine parts of the universe, where there aren't any stars. It turns out that we have now learned how to do that. We can look at light from stars and quasars, shining through otherwise empty regions of the universe, which are thinly dispersed with gas and dust.

So you have a back light that is shining through some primordial material, which has never been processed by going through a star or supernovae. So we can try to measure the abundances of light elements, in those primordial clouds, and try to compare them with the predictions of Big Bang nucleosynthesis.

The good news is, it works! The abundances we actually see in unspoiled parts of the universe, match the predictions of Big Bang nucleosynthesis. So here is an actual plot of some data versus some theoretical curves for what the predictions of Big Bang nucleosynthesis are, and what we observe.

We see predictions for helium-4, which we just call helium, deuterium, helium-3, and for lithium-7. No we'll notice that in this plot it's not just a single number prediction for each element, but a curve. There's some function, some parameter that is being varied to get different predictions. That parameter is the density of ordinary matter. So this plot, this set of predictions, assumes that we don't know ahead of time, the number of baryons in the universe, the number of protons and neutrons.

The plot is saying that as you change the number of protons or neutrons in the universe, we'll make different predictions for the amount of helium, deuterium, etc. There is a value for the number of protons and neutrons in the universe, for which we get the right answer. This is how Big Bang nucleosynthesis fixes the number of ordinary matter particles in the early universe. If there were more baryons in the universe, more protons and neutrons, you would make more helium. The production of helium would be more efficient. You would make correspondingly less helium, deuterium, and lithium-3, because you'd be getting rid of it into the helium.

So there's a prediction that if the helium abundance is higher, it means there are more baryons in the universe, but the deuterium abundance would be lower and so forth. There is a concordance, a match, between all the observations we have, and all the theoretical predictions, at one specific value for the abundance or ordinary matter in the universe. That abundance is 5% of the critical density, the density you would need to explain the spatially flat universe. So 5% of that, is existing in ordinary matter, baryons, protons, and neutrons.

So this is worth emphasizing, since it's one of the very crucial building blocks, on our road to understanding dark matter. We can measure the total amount of matter in the universe pretty efficiently, by using things like the rotation curves of galaxies and the dynamics of clusters of galaxies. We can find that there is matter there, and extrapolate it to the rest of the universe. In fact, we could imagine that we have missed some matter, something in between galaxies and clusters, yet we can't imagine that we've overestimated the amount of matter. The matter we see is certainly there.

So the total amount of matter we see is something like 30% of this critical density. Yet Big Bang nucleosynthesis provides a measurement of the total amount of ordinary matter in the universe, and it's 5%. It doesn't matter what happens to those baryons, those protons and neutrons, after Big Bang nucleosynthesis. They could get absorbed into black holes, they could collapse into brown dwarfs and other compact objects, they could be spread out in gas across the universe, they would all count in what Big Bang nucleosynthesis is sensitive to.

So it doesn't matter what form the baryons take, the fact that the predictions of Big Bang nucleosynthesis agree with observations of the abundances of the light elements, implies that the total amount of ordinary matter in the universe is not enough to be all of the matter in the universe. Not only is there dark matter, not only is there matter we don't see, but dark matter is not some hidden form of ordinary matter. It's some different kind of particle. That is the important implication of the success of primordial nucleosynthesis, for the story of dark matter and dark energy.

There are other implications we can get from the success of nucleosynthesis. For one thing, we mentioned that the process of nucleosynthesis was first, strictly dependent, very precisely, on the expansion rate of the universe at the time when it was just one minute old. Another is that the universe at that time was radiation dominated. The relevant amounts of radiation come from photons and neutrinos. Those are the light particles that were zipping around at very early times, dominating the energy density of the universe.

So if we changed the expansion rate of the universe by just a little bit, you would predict different things from Big Bang nucleosynthesis, and we would not get the right answer. How could you possibly change the expansion rate of the universe at different times? Well one way is you could change the value of Newton's concept of gravity. We have a constant that appears in Einstein's equation, so it reappears in the Friedmann equation. This constant tells you how strong gravity is. How much of a gravitational field, or how much curvature of spacetime is created by some amount of mass.

So this is a constant that has been around since Isaac Newton's time, and certainly describes how gravity works here in the solar system. The success of Big Bang nucleosynthesis is telling us that it is also successfully describing gravity, one minute after the Big Bang. Nothing dramatic has happened to change the strength of gravity. There's no reason to suspect that anything did, but now we know, based on data, that it didn't happen.

Another thing we know is how much radiation there is in the universe. If there was more of it, then the Friedmann equation would tell us that back then, during Big Bang nucleosynthesis, the universe would have been expanding more quickly. That would have altered the predictions of Big Bang nucleosynthesis. So for example, if there were not just three different varieties of neutrinos, and if there were four instead, with four different families of fermions in the standard model, that would be an extra contribution to radiation in the early universe. If there was such a fourth, light neutrino, then the universe would have expanded faster, things would have cooled off, and you'd get less helium, in contradiction to what you observe in the data.

So one of the reasons we're confident that only three families or generations appear in our standard model of particle physics, that we're not going to keep finding more and more families, is that Big Bang nucleosynthesis is inconsistent with extra kinds of neutrinos, as long as they are light, in the early universe.

So it's a little bit mundane when we think about nuclear physics, compared to dark matter and dark energy, but you should be impressed with the success of Big Bang nucleosynthesis. We take a bunch of laws of physics, all of which we've figured out in the course of the last 100 years. We're in a 14 billion year old universe, and we used these laws of physics to extrapolate back to what the universe was like one second after the Big Bang. We made a prediction, and it became right. That prediction turned out to be true! We know what the universe was doing a tiny fraction of a minute after the Big Bang.

It's like you're on a basketball court, standing at one end, and you try a hook shot with a blindfold on, at the other basket on the other end, and you hit nothing but net! It's that impressive, except that it's not an accident. You do it 100 times and you hit nothing but net every time. We're able to go from our knowledge of the current universe, all the way back then and get the right answer.

The reason why that's important for dark matter and dark energy, is because they are things we don't understand. Since there are so many things we don't understand in the universe, it's crucially important to have backup to the claims that we do understand something! The success of Big Bang nucleosynthesis tells us that we do understand the basic story of the Big Bang, and we do understand the basic equations that govern the expansion of the universe.

Our inference that the universe today is governed by dark matter and dark energy is buttressed by these facts. So now our job is to think about what those other things we don't understand, the dark matter and dark energy, could possibly be.