9. Relic Particles from the Big Bang - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

Now we can culminate our study of the laws of General Relativity and the Standard Model into theories and observations of the universe. We start by applying these laws to the early universe and compare the predictions with our current universe. This not only tells us if we are on the right track, but allows a glimpse on types of properties dark matter particles may have.

As usual, the course guide provides the raw technical details of the lecture, in this case the conservation rules of particle decay. What it lacks is the broader summaries from the actual lecture that tie everything together, though sometimes all too briefly. This is a fine example for one good use of these lecture reviews; the chance to document or discuss any missing or unclear material from the lecture or course guide. Some course guides are verbatim, so nothing is really left out. But I find this specific course guide to be woefully inadequate for really understanding the complex concepts of the course.

As the high temperature of the early universe cools over time, it will eventually equal the energy of the particles themselves and cease to create them. Those with more kinetic energy are hot and light, while those with more rest mass energy are cold and heavy. The lighter particles take less energy to create, so hot particles are more abundant. The massive particles take more energy to create, so cold particles are less abundant.

As the early universe expands, the particle/anti-particle annihilation decreases, allowing a freeze out of certain particles to occur. Neutrino/anti-neutrino pairs need to be very very close in order to annihilate each other. Over time they will be too far apart to interact. More of the weakly interacting particles survive and less of the strongly interacting particles survive.

The energy of the particles at the time of their freeze out creates two possibilities. If a particle naturally loses enough energy as the universe cools before freeze out, it will be a cold relic particle. If the freeze out occurs before it loses energy, it will be a hot relic particle.

Since we see dark matter clumping in galaxies and clusters, it must be a heavy, slow moving, cold relic particle. It also must interact weakly to have enough particles survive. Thus the acronym WIMP for weakly interacting massive particle. The next lecture discusses more specifics on WIMPs and alternate scenarios.

So by now, we know the laws of physics. When we say that, we mean basically all the fundamental laws from which all the rest of physics is derived We know General Relativity, Einstein's theory of curved spacetime, which manifests itself as gravity, and we know the standard model of particle physics. We didn't dig down into the quantum mechanical underpinning of the standard model, yet the standard model plus General Relativity is enough to cover every experiment we've ever done, and get the right answer.

Nobody believes these are the final answers to the laws of physics, yet as far as all the experiments we can do here on earth are concerned, they're good enough to match the data. The best indication we have that there's physics beyond the standard model and General Relativity, comes from the cosmos, from dark matter and dark energy, which we're trying to understand in these lectures.

So today, we'll take the laws of physics and put them to work in the universe. We're going to take the universe we see, the large universe that is smoothly distributed with galaxies, dark matter, and dark energy, and wind the movie back to the very early parts of the universe, plug in the laws of physics, and make predictions for what we're supposed to see now at the end of the entire process. Using the laws of physics and what we know about the early universe, what should we be seeing today?

In other words, we're going to be doing paleontology, essentially. We'll be looking for fossils, yet not the 100 million year old fossils in the ground, but the 14 billion year old fossils in the sky, these leftover particles from the earliest moments of the universe's existence. Partly this is just because we want to make sure we're on the right track. We think we have a picture that fits the data, and we want to use that picture to make predictions and then go test them.

Yet also partly we want to learn about what can come next. We think we have excellent evidence that there is early dark matter in the universe, for example. So the dark matter particles are going to be relics from the very early universe, and we need to understand how those particles are created, how the laws of physics can be used to predict how many kinds of particles of each kind there are. So we need to understand the different features of particles in different circumstances. We need to understand what particles do when they're by themselves, and what they do in a box with a whole bunch of other particles. Ultimately that box will be the entire universe.

So what we mean when we say "what particles do," is to either decay or be stable. It can sit there forever, not moving, or can turn into other particles. It can also bump into other particles, which would be relevant for the early universe when the densities are very high. So lets just think about particles decaying versus being stable.

Why do some particles last forever, and others go away? Well there are rules that govern when one particle can decay into some set of other particles. For our purposes today, there are basically two rules. One is that heavier particles decay into lighter particles. The second rule is that there are conserved quantities. There are numbers that don't change in any process of particle physics, including the decay of one heavy particle into a set of lighter particles. So lets put both of those rules to work in the particle physics we already know about.

The first rule says that heavier particles decay into lighter ones. This is basically a consequence of the conservation of energy. We know that mass is one form that energy can take. To a very good understanding, the energy of a particle is the energy in its mass, even if just sitting there, plus the kinetic energy of its motion through space. Those two forms of energy together tell you the total energy of the particle.

So if we have a heavy particle and ask what it can decay into, it can certainly not decay into an even heavier particle. There's no way for the energy of the final state to match that of the initial state. A light particle decaying into a heavier one, would violate the conservation of energy. So when a heavier particle decays into lighter particles, it can match conservation of energy, even if the masses do not precisely align. Since there's only a finite number of particles, it would be very surprising in fact that the masses of the first particle were exactly the sum of the masses of the second particles. The extra energy is taken up into kinetic energy of the outgoing particles flying away.

A classic example of an allowed decay of a heavy particle into lighter ones, is the decay of the neutron into a proton, electron, and antineutrino. We see that happen in nature, since the lifetime of the neutron is something like 10 minutes. So it must be the case that the mass of the neutron, the energy it has from E=mc², is greater than the sums of the masses of the proton, electron, and neutrino.

The neutrino is very light, so we don't have to worry, since it almost plays no role in this. Yet when we look at the numbers, the neutron and proton are both much heavier than the electron, with the neutron being a little heavier than the proton. In units of masses of the electron, the neutron is 1879 times as heavy as the electron. The proton is 1877 times heavier than the electron. So the neutron, 1879 electron masses, decays into the proton with 1877 electron masses, plus the electron, which is 1 electron mass, and get a sum which is 1878. This is still less than the 1879 that is the neutron, and that is why it's allowed to happen.

The fact that these numbers are so close, that the mass of the proton plus the electron plus neutrino is almost equal to the mass of the neutron, is one of the reasons why the neutron is so long lived. There are not a lot of possible arrangements for the outgoing particles.

Now consider the possibility of the proton decaying. What could it decay into? When you think about it, you might want the proton to decay into a neutron, a positron, and a neutrino. That would conserve electric charge, since the neutron and neutrino are neutral, and the positron has a positive charge just like the proton. Yet this event never happens since it doesn't match energy conservation. The proton is lighter than the neutron and therefor will never decay.

It's interesting to speculate that the universe would be a very different place if the masses of the elementary particles were a little bit different. What if the mass of the proton were a little bit larger than the mass of the neutron? Then it would be the other way around, and the neutron would be stable, with nothing for it to decay into. Yet the proton could decay into a neutron, spitting off a positron. What do all those positrons do, but go around and annihilate with all the electrons. In other words, we'd be left in a world with nothing but neutrons and neutrinos if the proton were heavier than the neutron. That would make for a very different world than the one in which we now live. There would be no atoms, no chemistry, no molecules, no anything like that. So we're very lucky that the mass of the proton is a tiny bit less than that of the neutron.

The second rule relevant to what can happen in particle physics, is that conserved quantities don't change. That's what the word conserved means. The most obvious example of a conserved quantity is of course, electric charge. It's sort of intuitively obvious to us that the electric charge shouldn't change in particle physics reactions. So for example, the electron for historical reasons has a charge of -1, the proton has a charge of +1, since it's made of three quarks , two up quarks with +2/3 each, and one down quark with -1/3 charge. The neutron is electrically neutral, just as the neutrino is, and comes from two down quarks at -1/3 each, and one up quark at +2/3 charge.

So in any process that can happen, the electrical charge of all the particles at the beginning, must equal the sum of the electrical charges of all the particles at the end. So for example, a neutron cannot decay into a proton, electron, and a positron. That would be allowed by energy conservation, but you would have a total charge of +1 at the end, yet a total charge of 0 at the start. So that is not allowed, and no one would have even guessed it to be, since we sort of understand immediately that electric charge is not created or destroyed.

Yet this is a good paradigm, a good example of something that happens and something that doesn't go away, and we have more subtle examples before us that play a big role in particle physics. The two other example we'll mention of conserved quantities of numbers that don't change in particle physics interactions, are quark number and lepton number. Basically the quark number is the total number of quarks. The lepton number is the total number of leptons.

The only subtlety there is that when we say the total number, anti-particles count as negative. So the difference between a particle and an anti-particle, is that all of the conserved quantities for the particle, are the opposite for the value of those conserved quantities for the anti-particle. So you know the electron has charge -1, and the positron has charge +1, since they are opposites.

Similarly, the lepton number of the electron is +1, so that of the positron is -1. The total amount of conserved charge for a particle and anti-particle will always add to zero and always be opposites. Quarks have quark number of +1, and lepton number of 0. There's no lepton number associated with quarks, just as there is no quark number associated with leptons. So then you add them up, inside a proton or neutron, and get a total quark number of three. There are three quarks inside a proton, therefor the quark number is three. Likewise for a neutron.

Remember that we defined different ways that quarks can get together to form heavier particles. We called a baryon any collection of three quarks. All the three different colors combined to give you one white baryon. So sometimes people talk about baryon number, which is exactly equal to quark number divided by three. So the baryon number of the proton is 1, since it has a quark number of 3.

Now consider the pion for example, which is a meson that's made of one quark and one anti-quark. So if you think about it, the quark number for a pion is 0, and likewise the baryon number also 0. So even though it's made of quarks, the total quark number is still 0. You can make as many pions as you want, you're not changing the quark number.

So the way to think about this is almost as if there's some stuff, some substance that changes its form, rearranges how it appears, yet is never created or destroyed. It's some nugget of quarkiness that can change from being an up quark to a down quark, or vice versa, as neutrons and protons intercommute, yet it never disappears. It never goes from being a quark to an electron, or something like that. So all the reactions we can possibly have in the universe will keep the quark number the same, as well as the lepton number.

Here is an example. You might think, if you were only thinking about electric charge, that the proton could decay into a positron, an anti-electron, and a neutrino. That would keep the electric charge constant, with +1 for the proton, a +1 for the positron, and 0 for the neutral neutrino. The reason why protons don't decay in the real world, is because quark number is conserved. So again this is a happy feature of the world in which we live, since if quark number were not conserved, the protons would all dissolve in to positrons which would annihilate. We'd be left in the universe with nothing but neutrinos and positrons, again not a very exciting place.

Likewise, lepton number tells you that certain things can't happen. Imagine a neutron trying to decay into a proton plus an electron. This is what people used to think that neutrons actually did. They saw the neutron sit there, and that the photon and electron would come out. The total electric charge is 0, before and after. The total baryon number is 1, before and after. The one neutron with three quarks turns into one proton with three quarks, plus an electron.

However we now know that this can't happen due to violation of lepton number conservation. There were no leptons before, and then there's an electron lying there afterward. That's why when a neutron decays, there must be an anti-neutrino involved. That anti-neutrino carries lepton number -1, so that the total lepton number at the end of the day, with the proton, electron, and anti-neutrino, adds to 0. So the neutron is allowed to decay, if there's that anti-neutrino there. It wouldn't have been able to decay if there weren't.

Now when we talk about historically, how do you invent these conservation laws? How do you figure out what is conserved and what is not? You don't do it by saying, "Aha, I think some number should be conserved, let me go look at the interactions!"

Usually you do particle physics, you measure what interactions actually do happen, which ones happen quickly or slowly, then try to figure out why certain things don't happen. That's how people come across things like the conservation of quark number or baryon number. People knew that baryon number was conserved, long before they knew what a quark was. They could see that neutrons didn't decay into neutrinos or something like that, so there must be some conserved quantity there. So that's how the game is usually played out.

Having said that, we should also admit that some rules are more solid than some other rules. Electric charge really is conserved. It is true that quark number and lepton number have never been seen to be violated in any experiments we've ever done, yet we wouldn't be all that surprised if someday we found that they were violated. In fact there are theories in which they are violated, it's just very slow that it happens so we haven't seen it yet.

Yet electric charge is something we really don't think is ever violated. If someone claimed to do an experiment and found electric charge created or destroyed, basically no one would believe them, unless they had some cache for some other reasons. It's something that no one expects on any theoretical basis. You can notice for example, that when you look at the whole universe and add up its electric charge, you get a number that is 0 as far as we can tell. There are an equal number of electrons and protons in the universe, so it's electrically neutral.

That is not true for quark number, and may not even be true for lepton number. The truth is we don't know, since we don't know how many neutrinos are out there, neutrinos versus anti-neutrinos contribute to the lepton number, and we can't count them. Yet we can count the quarks, which show up in protons and neutrons. There are many more quarks in the universe than there are anti-quarks. It could be that this is just how the universe started, so quark number is truly conserved and there has been this imbalance all along. Yet honestly nobody believes that. All believe that in the very early universe the quark number was 0, and there was some dynamical process that really did violate quark number, creating that imbalance.

That whole game that we try to play, creating quark number where there wasn't any before, is called baryogenesis, creating baryon number out of zero baryon number. We don't understand baryogenesis very well, so it's an open research project we'd like to understand better. Part of the ways we try to do this, is actually doing experiments here on earth that would witness baryon number being violated. There are proton decay experiments which conceptually are the simplest things in the world.

You get a big vat of stuff that is not radioactive, stuff that doesn't emit any form of high energy particles. You put it deep underground where no one will bother it, where no cosmic rays can come in and bump into it, and you wait for something to happen. You're waiting for something like a proton to turn into a positron plus a neutrino. That keeps electric charge and lepton number conserved, yet violates quark number. We've never seen it happen, but we're looking. As soon as we do see it happen, that will be a great advance in our understanding of the laws of physics.

So those rules are telling us what happens to a particle sitting all by itself, what particles can decay into others, and which ones are stable. Many of the particles we've talked about so far are stable. The neutrino, the electron, and proton, all are very stable. Why, if you think of it, can't we give any set of particles that those guys can decay into, while both being less massive and keeping all the conserved quantities conserved? The proton is the lightest particle that carries baryon number, that carries quark number, therefor it can't go into anything else! The neutrino is the lightest particle that carries lepton number, and the electron is the lightest particle that carries electric charge. So that's telling us why these particles can't decay. They have nowhere to go.

Dark matter is another particle which seems to be stable. One nice way to make new theories of dark matter, is to invent new conserved quantities that explain why the dark matter particle has lasted for the 14 billion years that the universe has been around.

Now lets take some of that understanding and put it together in the early universe where you don't just have one particle sitting there and decaying, but you have a bunch of particles. So the early universe is compact, things are squeezed together, the density is very high, and this means two things. One thing is that interactions happen very frequently, so particles are right next to each other and keep bumping into each other.

The second thing is that since the temperature is high, the energy per particle is very high. That's basically the definition of temperature, the average energy per particle. So if the energy of a particle is its rest energy, its mass, plus its kinetic energy, then when the energy is very high, the particles are moving all very quickly. This means that new things can happen.

Consider an interaction where a proton bumps into an electron. Now that interaction already happens all the time in a hydrogen atom. That's what a hydrogen atom is, an electron spinning around a single proton. You can ask what happens and the answer is nothing. The hydrogen atom can sit there forever.

Yet if we go to the early universe where the temperature was very high, instead of the electron just sitting there on top of the proton, we have an electron and proton running into each other with a large amount of energy. Then they can collide and turn into a neutron plus an electron neutrino. The total charge of that interaction goes from 0 to 0, quark number goes from 3 to 3, lepton number goes from 1 to 1, so everything is conserved. The only thing you're trying to do is add energy to the system so you can turn lighter particles, a proton and an electron, into a heavier combination. You can do that and conserve energy, if you're at high temperature.

So that's the kind of thing that becomes possible in the early universe when all the particles are zooming around very rapidly and bumping into each other. So this gives us a way of asking what can happen when you go from the very early universe when things are hot, dense, and bumping into each other, to the very late universe that we see today where things are very dilute, not bumping into each other all the time, and things are very cold. The universe right now, technically speaking, is not in what we call thermal equilibrium. We are not at the same temperature as the sun or the CMB.

Yet roughly speaking, when we talk of the temperature of the universe, the thing we refer to is the temperature of that CMB. That is the relic, leftover stuff, from the plasma that used to be in thermal equilibrium. In the early universe, those photons that we now see as the CMB, were rapidly bumping into everything else, and their evolution in temperature is what set the scale for how hot the universe is.

The way it works is very simple. As the scale factor goes down in the early universe, as things squeeze together, the temperature goes up. It goes exactly inversely, so when the temperature was twice as high, the scale factor was only half its current size. In particular, when the scale factor was 1/1000th its current size, the temperature was 1000 times as high, and that's when the CMB itself was formed.

If we keep going back, until the universe was very hot, then we can create new particles that aren't laying around today. Remember that the temperature is the rest energy plus the kinetic energy, the average total energy of the particles. So by increasing that temperature, by increasing the total energy, we have enough energy to create heavier particles than we find in the universe today. Whether or not they're stable, they will come into existence.

For example, an electron and a positron can come together and annihilate. We ask what would be the result, which would turn out to be any pair of particles and anti-particles, since the total of all conserved quantities for an electron plus a positron is zero. The total amount of conserved quantity in any "particle, antiparticle" pair, always adds to 0. So any "particle, anti-particle" pair, can always convert into any other "particle anti-particle" pair!

So lets imagine we invent a new kind of particle, called particle X. It's a fermion and comes with its anti-particle, the anti-X particle. The X particle is heavy, so we don't make it in the lab today, yet in the early universe when the energies were very high, electrons and positrons kept bumping into each other, and creating X particles and anti-X particles.

What we want to know is, how does the abundance, the density of those X particles and anti-X particles, change as the universe expands? So there are two events in the thermal history, in the lifespan of this X particle and anti-X particle. One is that it becomes cold. So if you think about it, the temperature tells you of the average energy of a particle, the energy is the rest mass plus the kinetic energy, and there's two different regimes you can think about. One in which the rest energy is much larger than the kinetic, and the other one in which the rest energy is much smaller.

If the rest energy is larger than the kinetic energy, that translates directly into the statement that the particles are moving slowly compared to the speed of light. They're more or less at rest, relativistically speaking. We call such particles cold. They're moving slowly and the temperature of the surrounding gas is small compared to the mass of that particle. In the other limit, when the temperature is very high, the particle's energy is dominated by its kinetic energy. This means it's moving close to the speed of light, and we call such particles hot.

So of course, as the universe cools down, the temperature of every particle goes down, and there will be a moment in its life when it goes from being hot, to being cold. That's the moment when the temperature, the average energy, is approximately equal to the mass of the particles. This is one important event.

Another important event is when particles freeze out. This is when particles stop interacting with the particles around them. Now in the early universe, not only is everything high temperature and high energy, it's also densely packed, close together. So things keep bumping into each other, and things can for example, annihilate. A positron will bump into an electron and annihilate, for example.

Today however, particles are more spread apart. Imagine that you have a positron here in this room, and you're in a strange situation where the nearest anti-positron (an electron) is a mile away. It's still true that if an electron and positron come together, they will annihilate, but if they're a mile away, they don't even know that each other exists. They can't find each other to annihilate.

So when things freeze out, and become so dilute that they don't find each other, they can exist even though there are both particles and anti-particles laying around. They could in principle annihilate, yet they can't find each other. They are left over as a relic abundance. It sounds unlikely for positrons and electrons, since they find each other very easily. Yet then when you talk about neutrinos, or other particles that interact very weakly, they need to be very close together to interact a lot. Neutrinos can freeze out very easily, since they interact so weakly that they stop finding anti-neutrinos and stop annihilating. That's the general picture.

The two different regimes, hot and cold, can happen at different times with respect to the event of freeze out. In other words, particles freeze out when they stop interacting, that's one event. The other event is particles going from being hot to being cold, and there's two different possibilities. You could first go from being hot to cold, and then freeze out. So you freeze out while you are cold, and are then called a cold relic particle. Or you freeze out while you're hot.

The only difference in these two different cases is how many particles you are left with. If you're hot and moving very close to the speed of light, your mass is very tiny compared to the energy that is going around. Then it's easy to make you, it's easy to make light, relativistic, particles. They don't weigh that much, so will be very abundant. When you're cold however, that means that you're heavy, you're massive, you're lumbering. It's hard to make X particles and anti-X particles if they're cold. Therefor if a relic is cold when it freezes out, there will be many fewer of them left around.

Now the obvious application to this kind of analysis is dark matter. You're going to say that you think there's a lot of dark matter in the universe. It's not a particle you see very easily, so could it be a leftover from some freeze out process in the early universe? This is where you start examining in detail the possibility that neutrinos could be the dark matter. They are the only particle in the standard model that could stand any chance of being the dark matter. They are neutral and weakly interacting.

So what happens to them in the early universe? When do they freeze out? The answer is they freeze out when they are hot. They are very light particles, so are almost always hot and moving close to the speed of light. So when they freeze out, they're hot and there's a lot of them. So we can calculate very accurately the number of neutrinos per cubic centimeter in the early universe, and extrapolate it with great confidence to the number of neutrinos in the current universe.

They could be the dark matter if they have a certain mass. We know very well what the mass of a neutrino would have to be, to account for the dark matter. Yet we don't think that this is right. We don't think neutrinos really are the dark matter, because while they're freezing out, they're hot, moving close to the speed of light, and therefor they don't clump together.

The characteristic feature that helps us find dark matter in the current universe, is that dark matter falls into galaxies and clusters of galaxies. We can measure the rotation curves of galaxies, and we find that most of the mass of the galaxy is dark matter. We can measure the speeds of galaxies within clusters, or use gravitational lensing, to find that most of the mass in the clusters of galaxies is dark matter.

Yet if the dark matter is hot, and moving rapidly when created in the early universe, instead of falling together under its mutual gravitational field, it would zip around and smooth everything out. The feature that you get when the dark matter is hot, is that structure doesn't grow in the universe. The dark matter particles are moving very quickly, and instead of falling together and becoming lumpy, increasing the contrast knob of the universe, the neutrinos or other relic hot dark matter particles would simply smooth everything out.

This is not a close call either. The possibility that the dark matter is hot, has been absolutely ruled out by what we know about the existence of galaxies and so forth in the universe. That's why, when we talk about the dark matter particle, we talk about cold dark matter. We talk about a particle that was massive when it froze out, that was heavy and moving slowly compared to the speed of light.

So what you want, is a particle that is heavy, and a particle that has enough relic leftover abundance to be the dark matter. If the particle interacted very strongly, there wouldn't be enough of it left over. It would just go away. If the particle interacts weakly, then you can make enough of it to be the dark matter. So that is why the leading candidate for dark matter is called the WIMP (Weakly Interacting Massive Particle). If it's weakly interacting, even though there are new particles X and anti-X particles, they don't annihilate away because they just don't find each other.

That is the leading scenario for what the dark matter could be. It's a cold dark matter particle, moving slowly because it's heavy, weakly interacting and therefor called a WIMP. That's a very general kind of scheme for what could be going on. In the upcoming lectures we'll look at specific examples for such things that can be leftover from the early universe. We'll look at specific examples of WIMPs to be sure for the dark matter, yet also more mundane examples like helium, something that we've actually detected. Even better than that, the CMB, all of which are going to give us very great clues as to what the universe was like in those early times.

8. The Standard Model of Particle Physics - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

As promised we now get more systematic as we step through the Standard Model of particle physics. This effort to characterize dark matter and dark energy seems to have started a new and large cycle on the atomic scale, eventually to return to the cosmological. The observations of last lecture now cycle back to the theory of this one.

Only three fermions and two bosons make up the grand total of visible matter, yet this is only 5% of the universe. Might the 95% be made of something from our Standard Model?

Lets face it, there are an overwhelming number of particles and forces with enough combinations of properties and symmetries to require categories of doublets, octets, groups, families, and generations. So I will only include highlights and conclusions.

The lecture and course guide presents the Standard Model well enough, and the appendix is also helpful so I won't duplicate that. But from early on and throughout, it hints that dark matter is not composed of any particle we are yet aware of. We are looking for a stable, electrically neutral, weakly interacting, massive particle not affected by the strong or weak forces. Dark energy is even from an entirely different model. So it seems this lecture and the last are just as much to prepare for the rest of the course on the big bang, as to tell us what dark matter/dark energy are not made of.

The important lecture material not in the guidebook is that of symmetry. The two doublets of the first fermion family pairs the up and down quark and the electron with its neutrino. Each pair turns out to be the same particle with a difference in charge. The up quark's charge of +2/3 is one off from the down quark's charge of -1/3. Similarly the electron's charge of -1 is one off from the electron neutrino's charge of 0. This hidden or broken symmetry is the reason for the Higgs field. Only at high energy, or high IQ, can we see it! This concept will be important later on when inflation is discussed.

The color of quarks has an interesting symmetry not documented in the course guide. As the electron's electric charge is the source of the interactions with photons, the quark's color is the source of the interactions with gluons. The quark color explains the combination of three different colors that make baryons, and the two same colors that make mesons. They all add up to no color, since the red, green, and blue make white. Also since any color plus its color from an anti-particle, also cancel each other.

The gluon is also made of color/anti-color pairs, but not necessarily of the same color. Red can pair with anti-red, anti-green, and anti-blue for a total of 9 possible pairs. Yet one pair doesn't seem to exist, so it makes 8 gluons in total.

More on conservation and symmetry in the next lecture.

In the last lecture we talked about atoms. There's a lot of different kinds of atoms that we know about. They make up all of chemistry and they string together to make up all of biology. We have a periodic table of the elements to explain how the different atoms fit together to make atoms. The remarkable fact is that an atom is just a different rearrangement of three different elementary particles, the electron, proton, and neutron, with the electron spinning around the proton and neutron in the nucleus.

Then we know that the proton and neutron are both made of smaller particles called quarks. You only need two kinds of quarks to make protons and neutrons, the up quark and the down quark. So you have three fermions that make up everything you've ever seen in the universe, the up quark, the down quark, and the electron. They're held together by two different kinds of bosons, the photon that carries the electromagnetic force, holding the electron to the atomic nucleus, and the gluon that keep the quarks together, inside the proton and neutron. So that's five kinds of particle that describe everything we've ever seen in the universe.

However, the theme of our lectures is that all that stuff, all that ordinary matter is only 5% of the universe. Who really cares about the 5% of ordinary matter? We're interested in the 95% that is the dark matter and dark energy, which we'll say later are not made of electrons, protons, and neutrons, not any arrangement of up or down quarks, or electrons for that matter. We need to find some new particle to make up the dark matter.

So in this lecture, we'll go through all the known kinds of particles. It turns out that there are more particles that exist, that we know about in nature, that we've discovered through doing experiments, than just the two quarks and the one electron. They fit together in nice patterns, and together all these particles and their patterns are called the standard model of particle physics.

So in this lecture, we'll go through all the particles of the standard model, a total of 12 different kinds of fermions, and 5 different kinds of bosons. We'll systematically point out why they can't be the dark matter, and no particle of course can be the dark energy, so we're stuck with that as a mystery as well.

When we're thinking about what could be the dark matter, it's something that is massive. It's heavy enough to be slowly moving. It's weakly interacting, which means it does not feel the strong force or the electromagnetic force, and it's electromagnetically neutral.

Of all the particles in the standard model, there are some particles characterized by those properties, namely what we call neutrinos. So we'll explain why in some detail, neutrinos are almost good enough to be dark matter particles, yet not quite. So lets get along because the standard model is so complicated, we'll start by giving away the punchline, telling us all the particles, then we'll back up and be a little bit more systematic, saying why we believe all those different particles are there.

We see a picture of all the different fermions in the standard model of particle physics. All the 12 different kinds of matter particles that make up what we find in particle experiments done all over the place. So we see that they come in patterns, with a set of three families, with four different fermions each. We see a pattern of four fermions, which is repeated two more times.

The lightest family contains all those three particles we've already talked about, the up and down quarks, and also the electrons. Yet there's a fourth particle there, which will be called the neutrino. The neutrino and electron together, make up a doublet (a pair) of fermions that are not quarks. We mean that these are fermions which do not feel the strong nuclear force.

So you have a nice kind of pattern in which there are four particles, where two of them form a pair that do indeed feel the strong nuclear force, and we call those quarks. Yet the other two form a pair that don't feel the strong nuclear force, the electron and neutrino, which we call leptons. That kind of makes sense, and then it's repeated again and again, which actually doesn't make sense! At this point in our knowledge of the universe, it's a complete mystery to us, why there are three families, or sometimes called generations, of elementary fermions.

Then you have the bosons, in the standard model of particle physics, which have five different types. We've seen two already, first the photon which is the most obvious particle in the world. It carries the electromagnetic force, and is responsible for all of chemistry through the exchange of these photons between different kinds of atoms. Then you have the gluons that will turn out to be eight different types, all carrying the strong nuclear force.

By the fact that there is something called the strong nuclear force, we'll probably have guessed that there is something called the weak nuclear force. This is carried by three different bosons, the W that comes in a positively charged type and a negatively charged type, and the Z boson that is neutral. So the W+, W-, and Z, are the three bosons that make up the weak nuclear force.

Then of course you have the graviton, the particle that carries gravity, which is the most obvious force there is. Yet the graviton is hard to find, since gravity is so weak and we have a difficult time decomposing the gravitational field into its individual particles. Yet the basic tenants of quantum mechanics say that it should be there, so most of us believe there is something called the graviton.

You may have heard that there are four forces of nature, which are the ones just described. The electromagnetic force with the photon, the strong nuclear force with the gluons, the weak nuclear force with the W and Z bosons, and the gravitational force with the graviton.

The fifth kind of boson in the chart, is called the Higgs boson, which does give rise to a force, just like the other ones do. Yet it's a little bit different since it has no spin, like the other particles, and most importantly it has not yet been discovered. So we think that there are five forces of nature in the standard model of particle physics, yet we've only found four of them yet.

So that's the general picture, so let's back up a bit and ask how we know, how do we get to the point that we believe in all these different kinds of particles? The neutrino in particular, doesn't feel the electromagnetic force or the strong nuclear force. When we say that a particle doesn't feel the electromagnetic force, we're saying that it's electromagnetically neutral, so it has no charge. The electron has charge -1, the up quark is +2/3, the down quark is -1/3, the neutrino is 0. So if the neutrino doesn't feel either the electromagnetic force, or the strong nuclear force, the question is how do you find it? Of course that's exactly the reason why it was the last of these four fermions to be discovered, since it's so hard to find.

It does however, feel the weak nuclear force. It turns out that every fermion in the standard model, feels the weak nuclear force, so that's how you find it. As a matter of experimental history, the way in which neutrinos were figured out, was through the decay of the neutron. It's a heavy particle, made of two down quarks and one up quark, yet is unstable. Left by itself, it will decay with a lifetime of about 10 minutes.

The reason why neutrons exist in nature in such abundance is that when you stick them together with protons, into an atomic nucleus, they can become stable. That's why some nuclei are stable and some are not, since you have to stick them together in exactly the right combination. Yet all by itself, the neutron sitting there will decay in a lifetime of about 10 minutes.

When people first observed these decays, they saw a proton coming out, and an electron coming out. That kind of made sense, since the neutron is a little bit heavier than the electron plus the proton together. The neutron is electrically neutral, and the proton has a positive charge which exactly cancels the electron. So it makes sense that the neutron would decay into a combination of a proton and an electron.

Yet when careful experiments were done, people measured the energy of the neutron ahead of time, and then the energy of the proton and electron that came out, and they didn't match. So when we talk about the energy, we're of course including the mass of the particle. We have a neutron at rest with an energy from E=mc², and then we add up the rest energy and kinetic energy of the outgoing proton and electron, and you get a number that is slightly less than the energy of the neutron that you started with.

So we're talking about early times, in the 1920s and 30s, when people were reinventing the laws of physics. Quantum mechanics had just burst on the scene, and we were in the midst of a revolution that was getting rid of most of Newtonian mechanics, on the basis of which we've understood all of physics for the last several hundred years. So people were willing to believe that cherished notions were ready to be violated.

So the first thing they did when they realized the neutron was decaying into a proton and electron, with less energy overall, was they said, "Well maybe energy is just not conserved?" Conservation of energy was something they were willing to do away with, to explain the decay of the neutron. Yet Wolfgang Pauli had a different idea, and asked what if energy is conserved, so that the other amount of energy we seem to be missing in this decay is coming out in an invisible particle? He invented such a particle which then Enrico Fermi called the neutrino. This was Italian for "little neutral one." The neutrino is sort of like the neutron, but much lighter, and still doesn't feel the electromagnetic force.

Now in this day and age, we've got a much more complicated theory of neutrinos, so Sean will just tell us ahead of time that the correct description of the decay of the neutron, is a proton, an electron, and what we call an electron anti-neutrino. The reason for the latter name will become clear over the next lecture or two, but it's a neutrino-like particle.

It turns out that Wolfgang Pauli was mad at himself for proposing the idea of the neutrino. He was actually kind of embarrassed because Pauli was an irascible, old physicist, who was famous for making fun of other physicist's bad ideas. Then he came along and suggested a particle that, as far as he knew, could never be detected. He thought of it as a kludge or mistake that tried to cover up something we didn't understand.

Yet these days, we do know better! We know there's an interaction that gives rise to the decay of the neutron into the proton, electron, and electron antineutrino. Therefor, since there is an interaction which produces the neutrino, it must interact. We're just much better now, at building detectors that are able to find very faintly interacting particles. So we have detectors that are able to discover neutrinos in large amounts. In fact we're able to measure their properties.

There's something called the Sudbury Neutrino Observatory in Canada, that actually looks at neutrinos produced by the sun, and looks at different types of neutrinos changing into each other. On the basis of this kind of experiment, we're able to measure that neutrinos have a small non-zero mass. When Pauli first suggested the neutrino, and Fermi developed the theory of it, they set the mass equal to zero, thus taking away its kinetic energy. Yet it turns out that today we know there's a tiny bit of mass in the neutrino.

We're still allowed to ask though, why neutrinos really exist? On one hand we can say that it hardly seems fair for there to be two quarks, the up and down, and only one lepton, the electron. Yet the neutrino completes a pattern. The up and down quarks belong together as strongly interacting particles that differ in electric charge by one. The up quark is +2/3, while the down is -1/3.

Now along with the neutrino, the electron is now a lepton that has a pair, so its other particle differs from the electron by one unit of charge. The electron has charge -1, and the neutrino has charge 0. So there's a pattern where you have two pairs of particles. It turns out that this structure is actually reminiscent, a remnant of an underlying symmetry that we don't see. In the deep down laws of physics, the electron and the neutrino are absolutely identical particles. The up quark and down quark, are also absolutely identical particles.

It turns out that the symmetry relating these particles is actually broken. It's hidden from us, so is a secret symmetry that is not obvious to us. You have to go either to very high energy, or very high IQ points, to figure out that there's some symmetry underlying this. That's the reason we know that either the Higgs boson or something like it exists, because the roll of the Higgs boson is to break that symmetry. We'll talk about that a little bit more later.

Still, even though the neutrino serves a purpose, the other fermions of the standard model, as far as we know, have no explanation. We have this nice structure where there are two quarks and two leptons, which fit together in a family. Yet then in studies of cosmic rays coming from the sky, Carl Anderson discovered another particle called the muon. It looked exactly like the electron, the same kind of interactions, the same charge of -1, and so forth. Yet it was heavier. No one knew how to fit it into the structure of the particles they already knew. It didn't fit into this nice pattern of two quarks and two leptons.

At the time we didn't know about the quarks, but we had the proton and neutron, and they formed a nice pair. Then people just kept finding new particles, so they filled in an entire new family. Along with the up and down quarks, we now get the charmed quark and strange quark. They are another pair of particles which form a doublet. Along with the muon, there is another kind of neutrino. So the old neutrino was rechristened the electron neutrino, while the new neutrino was called the muon neutrino.

Then it all happened again! Another pair of quarks, the top and bottom, and another pair of leptons, something called the tau and the tau neutrino. So there are these three families in the standard model of particle physics. We can see some kind of pattern there, and sounds like some sort of symmetry going on, yet nobody knows precisely what it is. The reason why there are three families of fermions in the standard model, is still a complete mystery.

Then of course we have the bosons of the standard model, the force carrying particles that can pile on top of each other, while fermions take up space so you can't squeeze them too close together. Bosons can pile on top to make a big, noticeable, classical field. So the electric or magnetic field are manifestations of many different photons piled on top of each other, and likewise the gravitational field is a manifestation of many different gravitons piled on top of each other.

So lets go through all the bosons in the standard model, and learn what we need to understand about the forces that hold the particles together that we see. So there is the photon of course, which carries the electromagnetic charge, yet is not itself charged. In other words the electric charge of the photon is zero, so it doesn't feel the electromagnetic force itself. It carries the electromagnetic force between other charged particles. So the electron and other charged particles exchange photons in an electromagnetic interaction, yet the photon itself does not interact with other photons. That's just a true fact about photons, not a fundamental fact of nature. Other bosons do interact with themselves.

For example, we have the gluons that carry the strong nuclear force. They are self-interacting, so they can bump together and interact with themselves. Yet they're much more complicated in their interactions than photons can ever hope to be, which is a little bit less natural and intuitive to us. So it's worth delving into the world of gluons to take a slightly closer look.

The important fact about gluons and quarks, the particles that feel the strong nuclear force, is that they are confined. The strong nuclear force is so strong that we are not able to separate any two particles that feel the strong nuclear force. This is not just because we don't have access to quite enough energy to pull these particles apart, but it's a matter of principle! You cannot pull apart to quarks, far away enough to they look like elementary particles all by themselves. Quarks will always be bound together inside bigger particles which we call hadrons, which are collections of particles that feel the strong nuclear force.

So why is it that quarks are bound together inside strongly interacting particles? The reason is that unlike the electric or gravitational forces that grow weaker with distance, the strong nuclear force grow stronger as you pull things apart. When close together they don't feel that much force, and they just zoom around. Yet if they try to separate, the force becomes stronger and pulls them back together.

So pulling apart two strongly interacting particles like quarks is like stretching a rubber band, and trying to get a rubber band with two ends to break, where you only have one end over here and another end over there. You cannot break a rubber band with two ends to make two separate ends that aren't connected to each other, because it snaps and you just get two more ends! Every time you have a piece of rubber band, there are always going to be two ends, so that you won't find one with just one end on it.

That's how the strong interactions work. If you pull apart two quarks, you will make a new "quark, anti-quark" pair in between, and they will snap off to make two more bound systems of quarks. You will never see a free quark or a gluon all by itself, because they are so strongly interacting. In fact, as a little preview, this idea that when you pull things apart and they snap like rubber bands, is the origin of the idea that instead of little particles, we're dealing with little loops of string. So if you chase that concept to its logical consequences, you end up with something called string theory. Yet this turns out not to be such a good theory of strong interactions, but is a good theory of gravity, as we'll talk about later.

So that's the important feature of quarks and gluons, their being confined. Lets think about into what kinds of particles they become confined. When people looked at all the different strongly interacting particles they could find, all the different hadrons they could find, they noticed the important fact that they always came in one of two varieties. Either they were made of three quarks, or one quark and one anti-quark. You never found a collection that was made of only two quarks, or two quarks and one anti-quark. It was always either three quarks or one quarks and one anti-quark. Of course three anti-quarks would work just as well as three quarks.

So they gave names to these particles, a baryon for those with three quarks, such as protons and neutrons as the classic examples. Both are made of three quarks each, so both are baryons. If something was made of one quark and one anti-quark, they called it a meson. The pion is the meson that carries the force between protons and neutrons inside the atomic nucleus, is a classic example of a meson.

So people started to wonder why we only found these two combinations of quarks in nature. Why is it that we only find particles with three quarks, or with one quark and one anti-quark? The answer is that you can assign to quarks a quality called the color. Since quarks come in three kinds, they will be either red, green, or blue. These colors act in the strong interacting world, like electric charge acts in the world of electricity and magnetism. The color of a quark is the source of its gluons, just like the electric charge of the electron is the source of its interactions with photons.

So the reason why it's very clever to assign colors to quarks, is because then you can then explain why you only get three quarks, or one quark and one anti-quark, by saying that you ever see colorless combinations of quarks as free particles! If you think about it, from how your tv works, if you have red, green, and blue shining, they appear as white light. You can combine them together to make white. You could also combine red and anti-red together to make a colorless combination. If you like, you can think of anti-red as cyan, anti-green ad magenta, and anti-blue as yellow. Yet most physicists forget that and just call them anti-red, anti-green, and anti-blue.

So a quark and anti-quark make a colorless combination, a red and anti-red, or a green and anti-green. That's why you get only these two kinds of visible particles made out of quarks and gluons. You must combine quarks and gluons together into combinations that have no net color. Those combinations are either baryons or mesons.

Gluons, sadly, are funny. They're a little bit difficult to explain, and every gluon carries simultaneously a color and anti-color. So you'll have a gluon that is labeled as green and anti-red, or blue and anti-blue, and so forth. So if you count in your head how many different possibilities, there should be nine:

red and anti-red
green and anti-green
blue and anti-blue

red and anti-green
red and anti-blue

green and anti-red
green and anti-blue

blue and anti-red
blue and anti-green

Yet one of these is missing. There turn out to be only eight gluons in nature, and this is one time in these lectures where we have to say, "You just have to trust me on this one." There are complicated mathematical reasons why that ninth gluon isn't there, the one combination that doesn't exist in the real strong interactions. Yet roughly speaking you can get pretty far thinking of the gluons that exist, as combinations of color and anti-color. So if you're going to join them together, you're going to still have to stick to that rule that we only see colorless combinations.

So those are the bosons we know, the photon and gluon, but what about the weak nuclear force? We mentioned it was carried by W and Z bosons. The Z is all by itself as a neutral particle, sort of like the photon, but it has a huge mass. The photon has zero mass, being massless and moving at the speed of light, while the Z boson is also electrically neutral all by itself, but very heavy. The W bosons are also very heavy, one positively charged and one negatively charged. Together these three kinds of particles carry the weak nuclear force.

In fact, the reason why the weak nuclear force is weak, is because these W and Z bosons are so very heavy. If you think of forces as being manifestations of bosons traveling back and forth, photons and gravitons, which are massless do so very easily. Gluons are also massless and travel only a short range, yet still travel back and forth very easily. Therefor all of these things can stretch over distances and still be very strong. Weak bosons, the Ws and Zs, are very massive, so it's hard to get them to travel from one particle to another. That's the reason why the weak nuclear force just doesn't seem very strong. It takes a lot of "umph" to make a W or Z boson.

In particular, lets think of an example of the weak nuclear force at work. There is one classic example, the decay of the neutron. One of the reasons why that neutrons last so long, is that the interaction which helps it decay is the weak interaction, which happens very infrequently. Neutrons last about 10 minutes, which might not seem long to us, yet to an elementary particle, it's incredibly long.

All these other particles of the standard model, which seem to be unstable to us, like the top or charm quark, decay away very quickly. The neutron lasts relatively long, because that decay of a neutron into a proton, electron, and anti-neutrino, is actually a manifestation of the weak interaction. So we saw a little picture of a decay of a neutron, into an electron, proton, and anti-neutrino, yet here is a magnified view of that picture. What is really going on is that one of the quarks inside the neutron, emits a negatively charged W boson, and in the process it converts from being a down quark into an up quark.

In other words, the neutron that was two downs and one up, becomes a proton of two ups and one down. The W that gets spit off, then decays into an electron and an electron anti-neutrino. So we have a better understanding of what happens when that neutron is decaying. It's really first emitting a W boson, which then decays itself. This is very paradigmatic of how modern particle physics works. We take an interaction that we see, that makes sense to us, yet to understand it better we zoom in on it and see other more complicated interactions going on inside. So those are the bosons that carry the weak nuclear force, the W+, the W-, and the Z boson.

There's also of course the graviton which carries the gravitational force that's so very obvious to us, keeping us on the ground. We ordinarily think of it, as Isaac Newton would, as some force traveling between massive bodies, or if we're Albert Einstein, as some manifestation of the curvature of spacetime. Yet if we're good quantum mechanists, we think of it as the exchange between us and the earth, of a whole huge number of gravitons. We're all certain that there exist such things as gravitons, which are just the quantum mechanical version of gravitational waves. Yet each individual graviton interacts so very rarely, it's almost impossible to detect it. So in fact, there's no plans in the immediate future, or what we should call the foreseeable future, to build a detector that would be sensitive to individual gravitons, even though we're sure that they are there.

Finally we have the Higgs boson, a little bit different from the others. The photons, gluons, and weak bosons, all have the same amount on intrinsic angular momentum. The graviton spins twice as fast as any of them, yet still is the same basic kind of idea. The Higgs doesn't spin at all, an absolutely spinless boson. Of course, it's purely hypothetical, and we haven't detected it yet. So sometimes we'll talk as if we know what the Higgs boson is like, yet what we really have is just a really good theory that predicts it's properties, but we're still trying to test that theory. We're very hopeful that the large hadron collider at CERN outside Geneva will find the Higgs boson explicitly, so then we'll be talking about their measured properties rather than just the hypothetical.

Why do we think there are Higgs bosons there? It's due to the story told earlier on the secret symmetry of the standard model. The secret symmetry between leptons, the electrons and their neutrinos, etc, and between the quarks, up, down, etc. We can understand all the interactions of the particles in the standard model if we promote the rough similarity between electrons and neutrinos and up and down quarks, into an absolutely true symmetry of nature. To do that, we have to explain why we don't see that symmetry, why the electron looks like it has a different electric charge than the neutrino.

The answer is because there is some particle, some field that exists and has a non-zero value, even in empty space. We call that field the Higgs field. It's almost like the Higgs is filling empty space with a kind of molasses through which these particles that would want to move at the speed of light, are slowed down from moving through this medium. The particles we have in mind are the W and Z bosons, as well as every single fermion in the standard model. All of these particles have mass, yet if it weren't for the Higgs boson, they would all be massless!

In yet other words, the understanding according to modern particle physics, of the origin of mass for all the fermions and the W and Z bosons in the standard model, is a hypothetical field called the Higgs field, which we haven't yet detected. Yet you can get an idea of why we're so very interested in detecting the boson associated with this field. It plays an incredibly important role in our understanding of particle physics.

So that's it. That's the standard model of particle physics. We have 12 different kinds of fermions, and 5 different kinds of bosons. So by now we can recall our mission throughout this whole project, which is to try and understand the dark matter and dark energy of the universe. Dark energy we don't think is even made of particles, but is a smoothly distributed energy density, about the same amount in space and time. We'll get to it in great detail of course.

Yet dark matter is made of particles. Could it be any of the particles we listed in the standard model? The answer is no. The thing we'd need to have to make a dark matter particle, is something that has a mass, yet is neutral and stable. The only stable and neutral particles in the standard model are the neutrinos. For a long time, people were hopeful we could understand dark matter as neutrinos. Yet the fact is that even though they do have a mass, it's still too small to be the dark matter. It's not so small that you can't get enough energy density to be the dark matter, but if you do, you have particles that are very light, yet moving close to the speed of light. That's not what you want in a good dark matter particle!

If the neutrinos were the dark matter, they wouldn't form galaxies and clusters of galaxies. They would come together as if they were going to do so, yet then just keep on going, close to the speed of light. You would not see in our universe, the galaxies and large-scale structure that we know to be there, if neutrinos were the dark matter.

So that's bad news in the sense that we don't know what the dark matter is, yet it's good news in the sense that 25% of the universe is something we haven't yet discovered. We will discover it as we look more closely, so in subsequent lectures we'll go into details about what that dark matter might be.

6. Gravitational Lensing - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture was less quantitative and more visual, which makes for a nice change of pace. But no less conceptual as the previous lectures, it demonstrates how observations of gravitational lensing confirm the Zwicky and Rubin conclusions of the need for a factor of five times the ordinary matter to account for dynamics of galaxies and their clusters. The more agreement the better of course, but lensing will play a role later in the course when trying to account for the composition of dark matter.

The best part of the lecture, and one of the best so far in the whole course, is the tale of the so-called Bullet cluster. This is actually two galaxy clusters nearby each other. The majority of the "ordinary matter" is in the form of x-ray gas, as expected. It's usually located between the galaxies of a given cluster, yet in this case it's located between the two clusters themselves, thereby implying a recent interaction. As when galaxies interact without affecting stars but only their interstellar gas, clusters interact without affecting galaxies but only their intergalactic gas. Gravitational lensing enables a rough map of the gravitational field, implying that most of the matter is centered around each galaxy cluster at the center of their own field.

These observations have two important implications. One is that most of the matter is not in the ordinary matter of x-ray gas, but is in some unseen form centered around each of the galaxy clusters. This is our good old friend, dark matter. Two, our current theory of gravity is correct, since some had suspected dark matter observations to just be a sign of a faulty theory. This also implies something about the charge of dark matter, since it did not interact like the charged particles of ordinary matter in x-ray gas did. Thus the world of particle physics is next on our plate in order to characterize dark matter and eventually, dark energy.

I want to make a comment about the appearance of so much knowledge about the universe. Ten years ago a similar type of course would probably have presented how much we had just discovered about the Hubble constant, solving the long and great debate between low or high values. A course ten years before that could talk about implications of dark matter, ten years before that the implications of inflation theory, etc.

Yet all along we had no clue about all of these recently discovered fundamental aspects, and I think we still don't. Dark Energy only shows us how much we don't know. But this has not been pointed out by Sean, so until he does, I will be a little disappointed about his bias. Robert Hazen's "Origins of Life" course does admit the ignorance of their field. In fact, Hazen's course is centered around this point of admitting ignorance. Though cosmology is the more experienced of the two, I believe both fields to be in the same state of just beginning to realize how much is unknown. I actually think this makes it all the more exciting! Please see my reviews on this "Origins of Life" course:

http://teachingcompany.12.forumer.com/viewforum.php?f=46

By now we're convinced beyond any plausible doubt that there is something called dark matter in the universe. What we've done is looked at the dynamics of bound systems, moving under their mutual gravitational fields. We've looked at galaxy rotation curves, the stuff moving outside galaxies, and we've looked at clusters of galaxies, large samples of hundreds of galaxies, and thought about both what the galaxies are doing, and what the hot x-ray gas in between the galaxies is doing. We find either way that you can't explain the motions we see, unless there's more matter in the universe than the stuff we can directly observe. So this should be evidence that closes our mind about whether there is dark matter in the universe.

Except that, of course, as scientists we don't like to close our minds until we really are as sure as we can possibly be. So in this lecture, we'll try to make another convincing case, from another completely independent set of information that points to exactly the same conclusion, that in galaxies and clusters, there's much more matter there, than the matter that we actually see.

What we did, when we looked at the motions of galaxies and clusters, was really mapping out the gravitational field of those objects. So again, when Einstein told us that whenever we have stuff in the universe, it creates a gravitational field. So we have a sure-fire way of finding everything there is. Just map out the gravitational field and use that to work backwards, to figure out how much stuff there is in the universe.

So we did that, but we'd like to do the same thing in a different way. We took advantage of the fact that particles, whether really individual particles or entire galaxies, move in a very determined way in the presence of a gravitational field. Yet they're not the only things affected by gravity. Even light itself is affected by gravity. That's part of the conclusion that Einstein was able to draw from the fact that gravity is the curvature of spacetime itself. Nothing escapes gravity's influence, so even a beam of light passing through a gravitational field, will be deflected.

This process of deflecting light due to gravity, is called gravitational lensing. We can use it as a completely independent way to figure out how much stuff there is in the universe. So the basic idea is simple. You take an object which gives rise to a gravitational field, and pass a beam of light past that object. The attractive force of gravity will bend the light ray as it passes by. In an extreme example, it can bend it quite a bit.

So we see an artist's impression of a gravitational lens that might be formed by a galaxy, with the thing being lensed as a quasar. That is a very bright nucleus of a galaxy, the center part of a very young galaxy, very far away and giving off a lot of light, so that they look just like points to us, like stars do. So quasar means quasi-stellar object, since originally they looked like stars. Now we know they're actually galaxy sized things in the very early universe.

So you look at a quasar far away, and you look at many of them until you get lucky enough to find an example of where there's a quasar far away, yet in between you and the quasar is a galaxy or cluster of galaxies, or something like that. If the gravitational field of the thing in between you and the quasar, is sufficiently strong, you can actually deflect that light from that quasar on both sides of the lensing object, and get multiple images, two images, of the quasar.

So this is something people have been looking for, for a long time. In the 70s and 80s they began to actually find them. So you can find pictures of this that look exactly the same astrophysical object, very far away. It's because there's something in between that is breaking up the image into multiple copies. You might ask how do we know that these two images that look the same, are really of the same object in the background? The answer is of course that we can take their redshift and find out how far away they are.

If you find two objects that look the same, and they're right next to each other, maybe with a little fuzzy thing in between, and you measure their redshifts and see they are equally far away, it's very likely that what you're doing is looking at exactly the same object. In fact you can do more than that. You can be more precise looking at the spectrum of light from that object and really verify that they are two different copies of the same thing.

So the reason it's called lensing is because it's the exact same kind of thing you would get when light passes through a piece of glass that is not absolutely uniform. If you have a piece of glass that is warped, that has different shapes, then the image of something you see behind it, will be distorted when you see it. You can do that correctly to make a lens that focuses on you or defocus, yet when you see any arbitrarily warped piece of glass, it will always give you distorted looking images. It's the same kind of thing, except instead of a piece of glass, we're now looking through a distorted spacetime, distorted by the stuff in between us and the stuff we're looking at.

This idea of gravitational lensing, of light being deflected as it passes through a gravitational field, goes back to Einstein himself. While he was working on his field equations, trying to derive the General Theory of Relativity, he was already thinking ahead. He was mostly coming up with the theory in his mind, through experiments, but was already thinking ahead to how we will know whether this theory is right? How will we test it against the data?

Of course we already had a theory of gravity from Newton which was really good. Everyone thought it was the best theory ever invented. Yet now Einstein is coming along with a different theory. There was already one piece of information that people knew about even before General Relativity, which is that the motion of the planet Mercury around the sun was not quit right. It was not quite moving in the orbit you would have predicted according to Newton's law of gravity.

So what do you do when something moves in an orbit which is not quite predicted by Newton's law of gravity, you invent dark matter! That's in fact exactly what was done. A French astronomer named Le Verrier invented an invisible planet that was supposed to be existing between the orbit of Mercury and the sun, which he called Vulcan. Unsurprisingly it was discovered several times, yet each time by mistake since it's not actually there. The idea was this new planet was a mass that was distorting the motion of Mercury, yet turns out not to be right.

It turns out that it was in fact gravity behaving differently. When Einstein invented General Relativity, one of the first things he did was to test what the orbit of Mercury should be like in his theory, and he found that it agreed. This was in Einstein's own words, the happiest moment of his life, when he realized that his new theory, fit this already existing data.

Yet he was also a good enough scientist to realize that it wasn't good enough to fit already existing data. You needed to make predictions for data that hadn't been taken yet. So as soon as Einstein invented General Relativity, he realized that the fact that everything is affected by gravity, means that even light will be so affected. This is something that Newton's theory didn't say anything about. So he was making a precise prediction that would be different in General Relativity versus Newtonian gravity.

However, the problem with his prediction was that it was very tiny. No one even knew about galaxies at the time, so Einstein was just thinking about stars, or perhaps the sun, which is the closest thing to us that is a large, massive object. Yet still the gravitational field of the sun in absolute terms, is just not that much. The amount of deflection that you get of light by the sun, is a very tiny angle.

There's an even more profound problem, when trying to use the sun as a gravitational lens, which is that the sun is tremendously bright. So if the sun is sitting there, and you're looking close by, hoping that it will lens some object through its gravitational field, the problem is you can't see any other objects, you just see the bright blue sky beside it.

There is one loophole to this problem of course, which is the possibility of a total solar eclipse. If you're lucky enough to be in the right place at the right time, when the moon goes in front of the sun, then the sun is still there, gravitationally lensing things behind it, still deflecting the light of stars that are nearby, yet suddenly you are not blinded by the sun itself. So if you take a picture of some stars in the sky and then wait until some future moment when the sun is in front of them, and there is a total eclipse, taking a picture of those stars yet again allows you to compare the image of those stars and positions on the sky, with the sun there and without.

If General Relativity is correct, the gravitational lensing effect of the sun, will distort the positions of those stars in your image, on the sky. So fortunately for Einstein, he invented General Relativity in 1915, and there was the perfect eclipse that was going to happen in 1919. Now of course by 1915, most people in the world, when you ask what was gong on in 1915 if they're physicists, will say that Einstein was inventing General Relativity. Most others will say that World War I was going on. So WWI ended a few years after Einstein finished his Theory of General Relativity.

So the eclipse came up in 1919, and an expedition was launched to make observations of it by Sir Arthur Eddington, a British astrophysicist and a very respected scientist in his own right. So he launched the expedition, went and took images of the stars in the sky, both before and after the sun was there, and he compared them. When he got back to England, they developed the film and realized that in fact, yes there was gravitational lensing of these stars. There was deflection of light by the sun, exactly as Einstein had predicted.

So what you had was a theoretical construction by a famous German scientist, being verified by an observation done by a famous British scientist, and it was actually taken at the time to be a very nice example of international cooperation among scientists, even though these countries were on different sides during WWI, they still agree that spacetime is curved, which is a good thing to agree on!

It also was the thing that launched Einstein's celebrity. Back in 1905, when he was inventing Special Relativity, Einstein wrote many papers that made him famous in the scientific community. Everyone by 1915 appreciated the genius of General Relativity, yet in 1919 when Eddington showed that the sun was deflecting light, just as Einstein had predicted, it made the front page of the New York Times. The general public suddenly realized that Isaac Newton had been superseded as the leading person to understand how the universe works, and Einstein took on that mantle. That was when he really became a public figure and often used his public persona to good purposes.

These days we go beyond just looking at the gravitational lensing of the sun, and use it as a tool to weight things. So the foremost thing we'll use it to weigh, are of course, clusters of galaxies, which we believe to be fair samples of what is in the universe.

There is another use that we'll just mention parenthetically, and get to in more detail in later lectures. That is to look for individual dark stars. If you have a dark star, some form of thing that is about the size of the sun, meaning anywhere from 100 to one millionth the mass of the sun, you can find those by using their gravitational lensing effect, because they move through the sky. So they're dark, but are moving through the sky and every once in awhile they will pass in front of a visible star. You can see the effect of the gravitational lensing on that visible star. It's very tiny, and is called microlensing. That's a way to find dark stars within our galaxy, which is something we'll talk about later when we discuss what the dark matter might possibly be.

Yet right now we're trying to establish that dark matter really does exist, so we'll use gravitational lensing to weigh clusters of galaxies. In other words, to map out the gravitational field of a cluster of galaxies in some detail. You can see, if you think about it, that there is an obstacle to doing this, that is not there for the sun or thee dark stars we might find via microlensing. The obstacle is that the cluster of galaxies is not moving in the sky. Both the cluster and whatever is behind it are sitting there on cosmological timescales, so even if you see something being lensed behind it, what you want to do is find out how much lensing there is, but you don't know ahead of time, where the object was. If the lens was not there, where would you see it in the sky? You can't compare before and after images, because nothing is moving, and the universe is more or less static over these very large distances.

So what you try to do, is figure out how much deflection of light you really have, even though you can't first put the lens there and then move it. You just have to deal with the fact that it's there. Well there's actually two different techniques that people have worked out to use, to figure out how much deflection of light there is. The first one was implicit in the first example we showed, the fact that you have strong gravitational lensing, is a lensing that is so strong that you see more than one image of the background object. Then you can figure out the angle by which it is lensed.

If you have one object in the background which passes through a cluster of galaxies, and you see two images of it, then there's an angle on the sky that is telling you the angle by which the light is being deflected. That is called strong gravitational lensing, and leads to some very pretty pictures that can show how strong the lensing is of some strong background galaxies.

The other possibility is weak gravitational lensing. This is actually much more common than strong lensing, where you're very lucky to find such a good example. Weak lensing is the idea that if you have a cluster of galaxies, and have a bunch of galaxies in the background, they will all be distorted by just a little bit. If you only had one galaxy in the background that passed through the gravitational lens, you wouldn't know what it was supposed to look like and where it was supposed to be, so it wouldn't help you in figuring out how much lensing is going on.

Yet if you have many galaxies in the background, their images will be distorted in a systematic way by the gravitational field of the cluster. So the fact that they begin to line up, not due to any intrinsic alignments, but because of how the light has passed through the clusters of galaxies, is going to be able to tell you how much lensing there was. So both of these techniques are in fact going to be used.

We see another image of a cluster of galaxies. We can see a couple of visible galaxies in the middle, and then also up and to the right, there is a bright red object which is an ancient star-forming region. It's an intrinsically interesting object all by itself, forgetting about dark matter and just thinking about astrophysics. This is some proto-galaxy that is coming to life, bursting with new stars and giving off a lot of radiation. It is in the background of this cluster of galaxies. We can measure its redshift and see it's very far away, and we see that it's distorted a little bit. It's aligned in a certain way that is sort of circularly wrapping around the cluster of galaxies.

So next we see an animation of how NASA scientists have been able to reconstruct the image of that star-forming region is distorted by the fact that it passes by the cluster of galaxies. So what you see is an initial image, giving off radiation. The light from that image passes by a cluster of galaxies, and as it does so, it is warped, going from a fairly square image at the beginning, to one in which it is distorted into this little ellipse.

We see yet another image, which is a reconstruction once again, of what would happen if we were to violate all the laws of physics, go faster than the speed of light, and travel from us here on earth, back to that star-forming region, going by the cluster of galaxies. What you see at first is the cluster of galaxies with the star-forming region in the background that's distorted into a little ellipse, and as you zoom past the cluster, what you see revealed is the original shape of the star forming region, which is actually closer to a rectangular shape than to this ellipse.

So you see that the effect of the cluster of galaxies, acting as a gravitational lens, is to change the shape of the background star-forming region. If you have enough examples of this, you can reconstruct how much gravity there was in the cluster.

So here is a more typical example of what you actually see with data. We see a cluster of galaxies once again, one we've already seen. Yet now we look more closely at it, in particular at the tiny galaxies on the outskirts of this cluster. Many of these galaxies are not in the cluster itself. They are behind the cluster and their light is passing next to it, on its way to us.

So what we see if we look at the galaxies in the background, is a systematic alignment of circles and regions of galaxies that are all little arcs. These arcs all wrap around the original cluster, due to the distorting effect of the gravitational lensing caused by the heavy gravitational field of all the mass in the cluster. You can see the number of arcs and the amount by which they're distorted.

If there were only one of them there, it might just be that this galaxy looked like an arc, all by itself! Yet if there are so many of them, there shouldn't be any reason why galaxies are lining up in such little arcs, especially if they are at different redshifts themselves. The reason why we see these little arcs, is due to the lensing effect of the cluster.

We know enough to take that data, the number of arcs and their distortions on the sky, to reconstruct from it, the total gravitational field of the cluster of galaxies. So we'll not be surprised to hear the answer, Sean hopes, which is that the total amount of mass needed to explain the amount of gravitational lensing, is five times as much as the amount of ordinary matter in this cluster of galaxies. In other words, the total mass that we've reconstructed by dynamical mechanisms, looking at moving galaxies and moving gas, matches, or is in correspondence with, the total amount of mass that is implied by gravitational lensing observations.

So this is nice and is telling us we are on the right track. If we didn't get that answer, it would have been very interesting. What if you have weighed this cluster of galaxies using two very different methods, but you're trying to measure the same quantity, and you've gotten a different answer. That would mean that you didn't understand something, either about clusters of galaxies, gravity, General Relativity, or something like that.

The fact that the two methods agree, giving us the same answer for the masses of these clusters of galaxies, seems to imply that we are on the right track. You can never be 100% sure that you are on the right track, since it's always possible you are being tricked one way or another. What happens is that as you collect more data, and get more examples of what is going on, the chances that you are being tricked, get smaller and smaller. At some point, it becomes a waste of your time to contemplate that you're being tricked, and you should just say, "Well now I have found something."

There are enough independent things pointing to the existence of dark matter in clusters of galaxies, that we've reached the point where either we should say that the dark matter really does exist, or that something even more profound is going on, something with gravity itself.

So lets look at one pretty picture, and then one profound example, both being hot off the press as new results in cosmology. The pretty picture is a three-dimensional map of the dark matter distribution in one direction of the sky. This is from the COSMOS Survey undertaken by NASA, and basically what they did is they said, "Lets take every telescope we have in all the different wavelengths of the electromagnetic spectrum, and point them at the same region of the sky."

So they took images with the Hubble Space Telescope, images in x-rays, infrared, radiotelescopes, ultraviolet images, and tried to reconstruct not just the picture of the sky in one direction, but the entire three-dimensional distribution of stuff. They have both the redshifts to different objects, and the images at each redshift. So what they can do from that, is reconstruct where the dark matter is. It's a little bit of a rough reconstruction. It's not highly precise, but you see the answer in this picture.

There's a distribution of dark matter throughout space. That distribution more or less matches where we see the ordinary matter. It matches it more than well enough, that we can say we are on the right track, so that where we think the dark matter is, is really where it should be.

On the other hand, it doesn't match it perfectly. So right now, one of the hot topics is research on things just like this, asking if the things that we see, which indicate that there is dark matter in a place where there is not a bunch of ordinary matter, is an indication of some novel mechanism in the evolution of galaxies and clusters that removes ordinary matter from dark matter, or if it's just that the data are not very good yet?

This is a kind of thing where we really don't know the answer yet. We're at the point where we do have a belief, a strong belief that there is something called dark matter, but the detailed dynamics of the dark matter and how it evolves along with the ordinary matter, is something we don't yet fully understand, and there's a lot more work to be done in that direction.

Now lets show Sean's favorite example, which is something called the Bullet Cluster of galaxies. It's a sequence of images of the same object, using different techniques. The first image is just a picture from the Hubble of this cluster. If you stare at it long enough, and you're a professional observational cosmologist, you will go "Aha, that is actually two clusters of galaxies."

There is a large concentration of galaxies on the left hand side of the picture, and the right hand side has a slightly smaller concentration. So you can actually take the redshifts and show they really are associated with each other, and are gravitationally bound. So this isn't just a chance superposition of galaxies at different distances.

So this is in interesting example of a double cluster of galaxies. There are two more or less independent objects, yet at the same redshift, so are right next to each other, cosmologically speaking. So remember we said that when we just think about ordinary matter in clusters of galaxies, forgetting for a moment about dark matter, in a cluster of galaxies, even the ordinary matter is mostly in between the galaxies, mostly in the form of hot, x-ray gas that is not concentrated in the galaxies themselves. Something like 2/3 or 3/4 of the ordinary matter is in this hot gas.

So when you see a cluster like this, especially one with an interesting shape, it's fun to take a picture of that cluster in x-rays and see where most of the ordinary matter is. So the next image shows us in pink, an x-ray image of this Bullet Cluster, a picture of where the ordinary matter is. It's glowing in x-rays and what you see is actually quite remarkable. The place where the ordinary matter is, shining in x-rays, is displaced from where the galaxies are. The ordinary matter is also coming in two clumps, just like the galaxies are, yet they are in between the clusters of visible galaxies.

Somehow the location of where the ordinary matter is, where most of the hydrogen and hot gas of this cluster is, is not in the same location as where the galaxies are. So this is interesting, yet it's not a complete mystery. There is a very simple explanation for how this could come to be. The explanation is that in the recent cosmological past, these two clusters of galaxies collided and went right through each other. You have to sort of think separately about the dynamics of the individual galaxies and of the dynamics of the hot gas in between.

The galaxies are fairly sparsely spread through the cluster. If you take the total area you see in a galaxy, it's only a tiny fraction of the size of the cluster as a whole. So when these two clusters went right through each other, came out the other side, the individual galaxies didn't even notice. They just went from one side and came out the other one. So you started with two groups and ended with two groups, perfectly the same and separate.

However, the hot x-ray gas inside these clusters of galaxies, does notice the hot x-ray gas inside the other one. So when these two groups come together and collide, there is a shock front set up, in the hot x-ray gas. The gas is slowed down from moving, but the fact is that it's interacting with the gas in the other cluster. So what we see is that basically the gas gets stuck in between, and you get a separation between where the galaxies are and where the gas is, in between.

That is of course, intrinsically interesting to astronomers, who would like to understand how clusters evolve in cosmological history. You don't get many examples of two clusters of galaxies passing through each other, so it's a lot of fun just to think about that.

Yet also from our point of view, we're interested in dark matter and dark energy, so it provides a unique opportunity to ask what the dark matter behaves like. If we believe that there really is dark matter in these clusters of galaxies, one of the features of dark matter is that it doesn't interact very much. This fact is most obviously displayed by the fact that the dark matter is dark. Most of the interactions over cosmological length scales of things in the universe, are either through gravity, which affects everything, or through electricity and magnetism, which affects charged particles.

So even atoms which are neutral, are made of charged particles, which is why we can see them. Dark matter is not charged, otherwise it would be easy to see, and they would not be dark. So the dark matter, to a very good approximation, is "collisionless." The dark matter particles go right through each other and do not bump into each other.

That's the reason why in an individual galaxy the dark matter halo is some big puffy thing, the bright visible stars have condensed and settled into the middle of this halo, because ordinary matter can bump into other ordinary matter, cool off, and settle down to the middle. Dark matter falls into a galaxy and just passes right through, so ends up in a big, puffy cloud while the ordinary matter settles into the middle.

So we want to know where the dark matter is in the Bullet Cluster? We started with two separate clusters, both with ordinary matter and dark matter. They passed through each other, the hot gas got stuck in the middle, so what did the dark matter do?

The next image is a reconstruction based on data of where the dark matter is in the Bullet Cluster. In particular, it's a reconstruction of where the gravitational field is in this cluster, based on gravitational lensing observations in the background. What we see is quite remarkable. The dark matter, or at least the gravitational field in this cluster, is centered on where the galaxies are. Yet remember that the galaxies are not centered on where most of the mass is located, which is in the hot gas in between the galaxies, and it was displaced. Yet the gravitational field stuck along with the galaxies.

The next picture superimposes where the gravity is located, and where the matter is located. The gravity is in blue on the outsides and the matter is in pink on the inside, giving off these hot x-rays. We see a very clear example of where the gravitational field in this cosmological object, is pointing in a different direction than where most of the "ordinary matter" is located. This can't be explained if you don't believe in dark matter! If you only believe in ordinary matter, the stuff that is causing the gravity, is the ordinary matter. So the stuff where the gravitational field is, should be where the ordinary matter is.

In fact, this is not only good evidence that there is dark matter in the sense that there's a lot more stuff than what we see, but it's also good evidence that we're on the right track when it comes to gravity. Up until now, we could always have believed that the reason why the gravitational field in an individual galaxy or in a cluster of galaxies is stronger than it should be, is because we didn't quite understand how gravity was working on large scales. Einstein and Newton were somehow going wrong on the scales associated with clusters and individual galaxies.

This Bullet Cluster result is telling us that that's not right. There is no way to understand how the gravity could be pointing in a different direction than the ordinary matter, if there was just a modified theory of gravity, but there's no actual dark matter. We'll discuss this result a lot more in future lectures, seeing whether you can get rid of dark matter and dark energy by modifying gravity. Yet right now we're confident enough to move on with the conclusion that there really is a lot of dark matter in our universe.