- Well, good evening and welcome to UW Space Place.  This is one of our guest speaker nights, and I would like to introduce Professor Ed Churchwell of the UW-Madison Astronomy Department.  Recently retired from that department, but he came to Madison from Germany from the Max Planck Institute in 1977 and has been here ever since, during which time he's done a lot of really important research here, primarily as a-- Well, I shouldn't say primarily.  As a radio astronomer, certainly, but here at Space Place you can see a lot of exhibits with Ed's fingerprints on them because he was very involved with the Spitzer Space Telescope and a project called GLIMPSE, mapping the Milky Way, the plane of the Milky Way galaxy.  So, I'm really pleased to introduce Ed tonight.  He's going to give us a talk on, basically, cosmology and how astronomers can figure out how the universe has evolved since its origin.  So, let's welcome Ed.  Thank you.  [applause] - Well, thank you very much for coming out, particularly on a rainy night like tonight.  This is a topic that I could spend a whole semester on, okay? So I'm going to try to distill some of the main components of what we have at our disposal to understand how the entire universe, in fact, has changed from the instant after it was born until the present time and on into predict the future. 

 So, hang on to your hats because you're going to go through a fantastic journey here.  And please, if you have questions, interrupt, and I'll be glad to answer them if I can as we go along.   Okay, Mark Twain once made this famous statement: "There's something fascinating about science.  One gets such wholesale returns of conjecture out of such trifling investment of fact." [laughter] And that was certainly an apt description of cosmology in the first half of the 20th century.  The idea that we can determine the properties of the universe as a whole, a tiny, tiny fraction after its birth, is presumptuous to say the least.  But, in fact, that's precisely what cosmology tries to do.  So, surprisingly, the history of the universe can be described based on six quantities that can actually be determined from observations, luckily.  I'm just going to kind of point out quickly what these are.  H-naught is what's called Hubble's constant.  It basically is a measure of how fast galaxies or clusters of galaxies are receding away from us as a function of their distance from us. 

 And that's a fundamental quantity, and it's one that's easily observed.  In fact, it was first observed in 1929.  The omegas here, one is omega sub R, it means for radiation.  It's the fraction of energy density in the universe in the form of radiation or photons.  And the naught here means that these are quantities that we measure at the present time.  So the naught means they're quantities we measure today, but if we can measure them today, we can project them back at any other time.  And that's a key issue, mainly because if we can establish that the universe was in thermal equilibrium, then we can determine all these parameters at any give time.  The omega M here is the fraction of energy density in the universe in the form of matter.  The omega sub lambda is the fraction of energy density in what we call dark energy.  I'll come back to all of these in a moment. 

 Q-naught is called the deceleration parameters.  So it's a parameter that determines what the rate of slowing down of the expansion of the universe is.  And basically it's not an independent parameter.  It really depends on omega-naught.  So if we can determine omega-naught, which is the sum of all of these three omegas I was talking about here, then we also know Q-naught.  And T-naught is the temperature of the universe as measured today.  So, let me move on now.  So, the observational underpinnings.  There are about six kinds of observations that have been made that actually determines these properties and tells us how to go about using those properties to say what the universe was like at any given time.  One is what's called the universal expansion, or Hubble's Law, which was first published in 1929. 

 He got H-naught a little wrong, but he certainly understood the principle.  The other is the abundance of the light elements of primarily deuterium and helium, and that was something that first kind of came to light in the 1950s.  And the others, dark matter, the detection of dark matter-- [beeping] Is that me? - No.  - Oh, sorry.  The light's in my eyes.  I'm trying to move out of the light.  So, dark matter was first actually detected in 1933 by a Swiss astronomer who was working at Caltech at the time.  He was looking at the motions of galaxies and a cluster of galaxies and realized that they were moving a lot faster than they should be moving based on the amount of light that they were producing.  In 1939, another astronomer I'll get to in a moment also found roughly a similar sort of thing, but basically by measuring the rotation rates of spiral galaxies.  And he found they were rotating much faster than they should. 

 And then, in the 1970s, Vera Rubin did a very detailed study of the rotation of galaxies and basically found that the only way you could understand the rotation rates is if there was more matter there than you could actually see from the light that's produced by stars.  I'm going to go through these a little bit more in a moment.  So the large scale distribution of matter over the cosmic microwave background.  Let's come back to that. That's an important one.  It was first detected almost by accident in 1965 by two radio engineers, actually, at Bell Labs.  And basically what they measured was the temperature of the universe at present time.  Then the large scale distribution of matter, that is how clumpy is the matter distribution on the universe? And it turns out that it's not smooth, at least on what we call from an astronomical point of view, on a small scale.  Large enough scale and it looks pretty smooth, but it ain't necessarily so.  The recession velocities of type Ia supernovae is used-- Those are standard candles.  There's objects that have well determined intrinsic brightness, and so if you have that, you have a standard candle so that you can determine from the apparent brightness and you can determine what the distance is. 

  Okay, so I'm going to-- Those are the six kind of main observational underpinnings.  And I'm just going to quickly run through this.  Universal expansion basically was done by Hubble and Humason in 1929, and they found that velocity, the recession velocity you can measure through spectroscopy is basically just proportional to the distance of the galaxies.  And so this H-naught is the key parameter here.  So if you just take the velocity which you can measure and you have to be able to measure the distance independently in some way, but there are ways to do that.  And so H-naught is this V over D.  And so that's what was used to determine this.  This result, however, implies that the universe is much, much smaller in the past, i.e. the mass densities are much greater than they are today.  Also, if the universe is expanding and you're not changing the total energy in the galaxy, what happens when you take a gas under pressure and you let the pressure off? What happens to the temperature of the gas? - It drops. - It goes down, right? That's exactly the same thing that happens in the universe.  The universe started out as something incredibly dense and hot and massive and then it has been expanding ever since. 

 At one point it was explosively expanding.   And so, as it expands, it also is cooling down.  And so that's the key component of our understanding of the evolution of the universe.  Expansion here, you got to be careful.  It doesn't mean-- It's not like the motion of galaxies through space.  It's space itself that's expanding.  Okay, so it's like the-- There are several examples that have been given that people use, but one is if you have a loaf of bread with raisins in it, you start to cook the bread and the bread rises, the relative positions of the raisins don't change.  They only change in their separation, right? But the pattern doesn't change.  And this is the same sense we're talking about for the universe, that it's space time that is expanding not the motion of galaxies through space.  Think about that. 

 Okay, abundances to light elements.   Those elements, deuterium, helium, can only be understood if the early universe was hot and dense enough to have been a thermonuclear furnace, and therefore have cooked the hydrogen atoms and produced helium and deuterium.  The stars can't produce enough of this to-- of the amount that we actually see.  Okay, so-- And this is consistent with the idea of the expansion of the universe.  If you go back in time, the universe had to be hot and dense, and at some point it had to go through a period where it was dense enough and hot enough to actually behave like a thermonuclear furnace.  Okay, Alpher, Herman and Gamow, based on the realization that the universe was hot and dense enough to sustain nuclear reactions to convert hydrogen to helium and possibly heavier elements in the 1950s.  And they actually even predicted roughly what the temperature of the universe should be today.  And they estimated somewhere at five to seven degrees Kelvin.  You'll see in a moment that we have a very precise number for that now, and it's about three degrees.  Dark matter, Fritz Zwicky in 1933 found that the velocities-- I've already gone through this, so I'm going to zip through it fairly quickly. 

 You see, though, there were several players in this area.  Vera Rubin, in the '60s and '70s, basically did a systematic study of the rotation of spiral galaxies and concluded that there's a lot of unseen matter in the universe that we don't see with our telescopes.  This is the idea, however, right here that if you look at the rotation rate of spiral galaxies from the center of the galaxy outward in radius, what you would expect if all the matter was confined to the nucleus of the galaxy, it should go like the curve eight that I show here.  This is how the planets move around the sun.  They go as one over R-- One over R to the one-half power.  But that's not what happens.  They actually-- The rotation rate stays up here flat, much higher rates of rotation as you go outward than you would expect.  And the only way that can happen is if you're enclosing more and more matter as you go further out in radius on these spiral galaxies.  Okay, cosmic microwave background.   The radiation temperature of the universe today is about 2.735 plus or minus 0.005 Kelvin. 

 We know that very precisely now because basically the Planck, the COBE satellite in the 1990s.  But anyway, the fact is that you can look in this direction, this direction, any direction in the sky, and you get exactly the same temperature or you get exactly what's called the Planck function.  It's a function that tells you the brightness as a function of wavelength.  And we know that very precisely, and I'm going to show you here.  So the cosmic microwave background is really a picture of the universe when it was about 280,000 years old.  Okay? This is-- You can look back into space, and at some point you run into a wall where the universe becomes opaque.  You can't see any deeper because it becomes opaque.  And, at that point, if you take a map of the sky, what you see is, you know, this microwave background that's only about 2.73 degrees.  But when it's 280,000 years old, it was very, very hot.  But today we see it for only three degrees because the stretching of space time has stretched out the wavelength now to where it's equivalent to about three degrees. 

 Okay, so-- And it also-- Oh, an important thing.  That tells us, however, that the universe was in complete thermal equilibrium at that time.  So we can use this idea, you know, using basic physics, to trace back in time, or go forward if we wish.  Here, just to let you get an idea, though, of how precise a measurement this is.  This is one of the most precise measurements you're going to see in the natural world.  The dots that you see in that curve are measurements from the COBE satellite.  The curve is a Planck function.  It's the theoretical function for the brightness of an object at a given temperature.  Take a bar of iron and heat it up and it goes from very dull red to a bright red to a yellow to white.  And that's a Planck function, okay? And it's determined entirely by one quantity: the temperature. 

 It doesn't matter what it's made out of, anything else, except the temperature.  So that's the curve of the brightness of the universe as seen today.  And it peaks at about two microns.   Or two millimeters, I'm sorry.  Okay, so here's a picture of the universe or of the cosmic microwave background when it was about 380,000 years old.  And you see all these orange or reddish dots are a little bit warmer.  The green, intermediate, and blue is a little cooler.  But the amount of deviation from a single temperature is tiny.  It's in the 10 to the minus four.  One-ten-thousandth from top to bottom here. 

 So these are little ruffles which ultimately later on are going to become galaxies and things like that.   So a view of the universe.  I've just shown you one at about 380,000 years.  Going back even further in the past, the universe is basically just a hot thermal cauldron of subnuclear particles.  And then, if we go to present day, the universe looks like the bottom picture there.  So this is kind of a very quick thumbnail picture of the change in the universe.  But a lot of changes have occurred and I want to go through a few of those.   As I said, one of the other things that we want to know is the distribution of matter.  How clumpy is the matter that's distributed in the universe, and on what scale? And, basically, ultimately what happens here, as we'll see, is if you're thinking about the universe as space time expanding with time and gravity operating with this expansion, what happens? Well, a lot of simulations have been done, and basically what should happen is that matter starts to form into a filamentary structures and things like that.  And so it will not be smooth. 

 Matter tends to want to gather together with gravity.  And so we want to know if that in fact is what happens.  And these are observations now of galaxies.  And there were three surveys here.  This inner one had a fairly wide angle.  And all of these little yellow dots here are galaxies.  And you see that they're not smoothly distributed.  They are kind of filamentary.  And there's a second survey that was a little bit narrower piece of sky but going deeper, and you see that, again, matter is not uniformly distributed.  Galaxies are not uniformly distributed. 

 They're in kind of filamentary structures.  And then an even deeper survey where you start to run out of galaxies out there, not because there aren't any there but because it's a sensitivity issue that you can't detect these very distant galaxies so easily.  But you see again, no matter where you look, the distribution of galaxies is not smooth.  It's filamentary.  But, of course, if you add this up over a long distance, a large enough volume, the universe does look kind of uniform.  And that's important because all the relationships that we use make two assumptions.  One, that the universe is isotropic.  That means it doesn't matter which direction you look, it looks the same.  And it's uniform. It is uniform density.  And, as I say, you've got to now think, however, cosmically in order for that to be true. 

 This is a simulation using basically just the idea of expansion of the universe and cooling and gravity, and this is what simulations tell you you should see.  Okay, what are the tools needed to understand the evolution of the universe? Well, applications of well established physics.  Nuclear physics, high energy physics, relativity, thermal dynamics, and so forth.  But none of these are things that are mysterious or not understood.  So we can understand the universe using pretty straightforward physics.   One of the key ones here is what's called physics of annihilation and pair production.   An annihilation, it turns out, is independent of temperature.  It doesn't matter.  Once the temperature becomes low enough, some particles will annihilate with their antimatter particles.  Matter and antimatter particles will annihilate each other. 

 And if there were equal numbers, we would not have anything left in the universe.  It would all be in the form of photons.   Pair production is strongly dependent on temperature.  Pair production is when you have two photons that collide with each other, and if they're energetic enough, they will produce a matter and an antimatter pair particle.  But they've got to be hot enough-- The particles have to be moving fast enough or have to be hot enough to be able to have the equivalent energy of the mass particles that's produced.  And so, basically, the temperature has to be greater than-- It's proportional-- Greater than some factor times the mass of the particle that's actually produced.  That's the key.  So one of these is incredibly dependent on temperature.  The other is independent of temperature.  And so this makes for an interesting evolution of the universe. 

 So these threshold temperatures, the neutrons can be produced by colliding two photons together that as long as the temperature is greater than about 10 to the 13th Kelvin.  Protons are a little less massive, and they have to be hotter than about 1.088 times 10 to the 13.  So there's not much difference, but there is difference in mass and therefore the difference in the threshold temperatures.  Electrons, of course, are much less massive.  And their threshold temperature is substantially lower.  It's about six times 10 to the 9th or six billion Kelvin.  Okay, so the cause of a temperature today implies the temperature in the past when the universe was much smaller and denser, much hotter and much denser than today of course.  And you can infer the temperature back to a very, very small fraction of a second.  Temperature is basically just proportional to-- It should be one over the square root of the temperature here, of time, of age of the universe.  So it should be a square root over the T, the little t. 

  Okay, so the equation of motion that includes all of the constituents of the universe.  That means baryons and dark matter, radiation, neutrinos, dark energy and so forth, can be solved, and we'll come to that in a minute.  So let's talk about the evolution of the universe.  In the earliest point at which we can say anything at all about the universe is about 10 to the minus 43rd of a second.  Okay, so that's like a dot with 43 zeros after it and one.  So it's a tiny, tiny fraction of the universe.  But, believe it or not, we think we know roughly what the universe was like at that point.  We can't say much beyond that.  The reason is because we're not sure how the forces of nature, for example, were.  I mean, the presumption is that the four forces of nature were basically just a single force at this time. 

 We don't know how those subnuclear particles would react with each other under these temperature and density and with the knowledge of-- For example, we don't know enough about gravity at that stage.  So, that's the earliet moment we can determine the properties, and we're not sure how particles interact with each other.  Okay, but we can say one thing: that the universe at this instant had to be made entirely of fundamental particles.  That is, the particles that can't be reduced any more.  And what are those? Well, they're electrons, neutrinos, quarks, and they're antiparticles and photons and possibly gluons.   Okay, we're going to now go to a time of about 10 to the minus 32 seconds.  This is what's called a period of inflation.  Temperature is about 10 to the 21 Kelvin.  The temperature here is too high for protons and neutrons to be stable.  So what you have are these free quarks that are moving around in space at very high velocities and very high densities. 

  And if you form a neutron or a proton, they'd be broken down immediately because they're being banged into each other at such high energies.  The universe has cooled from the time that I told you, 10 to the minus 43 seconds, by about a factor of a million or so and increased by size by tens of orders of magnitude.  Now, the universe at this time has basically explosively-- It's started to explosively expand.  Nobody understands exactly why this is true, but it's called the period of inflation.  And the universe expands at a rate that is faster than the speed of light.  Now, you may ask, how can that be? Well, remember, we're not talking about motion of particles through space.  We're talking about space itself.  The rate at which space can expand or contract is not controlled by the speed of light.  Okay, by the theory of relativity.  And so the universe must have gone through this period of what's called inflation where it may have expanded by, you know, like, 25 orders of magnitude in, you know, a tiny, tiny fraction of a second. 

  So, quarks and antiquarks are beginning-- By the way, quarks are these particles.  They're very strange particles, but they are fundamental particles as far as we can determine.  And protons and neutrons are made of combinations of three different quarks.  There's another set of particles called mesons that can be formed out of combinations of two quarks.  But at this point, they're free particles.  And that's something that we'll probably never see again in nature.  Okay, so they're beginning to be bound into protons and neutrons and they're antiparticles.  As a consequence, they now undergo what's called freeze out.  That is, they no longer are going through-- They don't go through a period of annihilation and pair production.   The precise time when this occurs is not all that well established yet. 

 And I'm not going to say anything more about quarks.  Now we're going to jump down to 10 to the minus 12 of a second.  Temperature now is about 10 to the 15th Kelvin.  It's a factor of a million cooler than that other time point.  Quarks have combined to form protons and neutrons and mesons and their antiparticles, leaving no free quarks.  Electrons, neutrons, protons, neutrinos, and their antiparticles are stable and freely interact with radiation, and so you have pair production and annihilation that's going on at exactly the same rates.  So they're annihilating each other and being formed through pair production at equal rates.  And so it's a stable, completely-- What's the word I want to use here? - Zero sum? - Well, zero sum would be a good term.  They were in equilibrium.  That's what I really want to say. 

 Okay, so now we're going to jump down to a hundredth of a second.  Temperature now is about 10 to the 11th Kelvin.  This is below the threshold temperatures of neutron and proton pair production.  And so they're rapidly disappearing from the universe.  Because they no longer can be formed by pair production because the temperature is getting too low, but they can annihilate each other.  And they keep right on annihilating until there aren't anymore.  And so protons and neutrons are disappearing.  And the only thing that saves them is the fact that for some reason that we still don't understand, there was just a tiny little bit more matter particles than antimatter particles.  And so all the antimatter particles disappear, and you get a tiny residual of matter neutrons and protons.  It's about one out of every billion particles. 

 So, this is a key issue.  Now, the-- So what we call-- When this happens is what we call freeze out.  The universe has gotten too cold to make more of these particles out of photons.  And so they freeze out from the universe.  And to begin with, the number of neutrons is about equal to the number of protons, but neutrons, when they're not in an atomic nucleus are unstable and will decay at something like 11.7 minutes or something like that.  And it produces a proton and an electron when it decays.  And so you start to see then a change in the neutron to proton ratio.  And this is important because that will ultimately determine how much helium the universe will be able to make.   Okay, so the density of the universe is about 3.8 times 10 to the 9th grams per cubic centimeter at this time.  And if Mt. Everest were made of matter this dense, it would actually just destroy the Earth by tidal forces. 

  Okay, the doubling time for the universe is about two-hundredths of a second.  And at this time, there are about a billion photons, electrons, and neutrinos for every proton and every neutron.  Okay? The size of the universe we don't really know, but we can say that the universe at this time was something like 300 billion times smaller at this time than it is today.   Okay, you go to a tenth of second, temperature now is reduced to about three times 10 to the 10th Kelvin.  Contents of the universe now is electrons, positrons, and neutrinos, antineutrinos, and photons.  Protons and neutrons and their antiparticles have essentially disappeared, leaving behind this tiny residual of about one billionth.  So, you know, they're less than one billionth of their original number.  Let me just move on.  All particles are still in thermal equilibrium.  They have the same temperature and temperatures as the above threshold temperature. 

 I'm just going to go through this fairly quickly.  The doubling time of the universe now is about two-tenths of a second.  So you see that the universe is already slowing down in its doubling time or its rate of expansion.   And it continues to slow down because the universe is expanding against its own gravity.   And the temperature and matter density continue to decrease as time goes along.  And the neutrons are starting to get out of equilibrium or out of-- They're getting fewer neutrons than protons with time.  Now, at about 10 to the 10th Kelvin at about one second, the threshold temperature of electrons and positrons now are beginning to annihilate more rapidly than they can be formed through pair production.  And so electrons are starting to disappear.  It's still too hot for neutrons and protons to combine in an atomic nuclei.  So these are all just subnuclear particles. 

 Nuclei can't hold together at these high temperatures and densities.  The density is about four times 10 to the five grams per cubic centimeter.  Water has a density of about one gram per cubic centimeter.  So, this is three times 10 to the five times more dense than water.  Doubling time is about two seconds.  A decrease in temperature has allowed the proton to neutron balance to become 24% neutrons and 76% photons, or protons, I mean.  Now we go to about 13.8 seconds.  The temperature is about three times 10 to the 9th K.  Here we're below the threshold temperature for electron and positron production.  And so they are rapidly freezing out as well. 

 So now the electrons are disappearing as well.  And this does add some energy.  Each annihilation adds about a half a MEV of energy, which actually raises the temperature of the universe by a little bit.  Okay.  Neutrinos and antineutrinos at this time are more or less decoupled from the rest of the universe.  They no longer interact with normal matter.  And, you know, there's about a billion of these neutrinos that goes through my fingernail while I'm speaking at this instant almost.  There's a lot of neutrinos, but they don't interact with us, and so we're completely mostly unaware of it.   Okay, so let's see.  So from now on, when we talk about the temperature of the universe, we're going to be talking about the temperature of the gassiest components of the universe. 

 And temperature is still too high for atomic nuclei to be stable, and neutrons are still decreasing with time.  So we go to three minutes and 45 seconds.  Temperature is now about nine times 10 to the 8th Kelvin.  Still very hot.  Deuterium can become stable, but unfortunately its binding energy is not able to withstand the bombardment at these high temperatures.  And so it doesn't actually form at this.  It could with as far as the temperature is concerned, but-- I'm mean, sorry.  It couldn't because the temperature is still too high, the bombardment energies are too high.  Okay, if you just plot as temperature versus mass, there's this short period where all these light elements can be formed.  And this kind of started out with protons and neutrons, and at this point in time, our temperature of about 10 to the 9th Kelvin, all these things get to be made and it's over a very short time. 

 Okay, 34 minutes and 40 seconds.  We have a proton dominated universe.  Temperature is about three times 10 to the 8th.  Matter density is now too low to support nuclear processing, even though the temperature is high enough.  All elements capable of being produced in a big bang have been made.  The electrons and protons or electrons and positrons have been completely annihilated, leaving only a small residual of about one in a billion of the original number.  The same as protons and neutrons.  And that's-- This tiny residual is why we're here because there was this imbalance, and, as I say, we don't really quite understand why that imbalance was there.  Okay, so the consistency of the universe now is photons, neutrinos, antineutrinos.  Density is about 10 grams per cubic centimeter. 

 And of this density, about 31% is in neutrinos and 69% is in photons.  Okay, I want to kind of move on because I'm going to run out of time here.  So, the doubling times now of the universe is up to about one and a half hours.  Every one and half hours, the universe doubles in size.  Okay, seven times 10 to the five years.  So we're jumping along.  This is called the Dark Ages.  Temperature now is reduced to about 3,000 Kelvin.  At this temperature, the universe is cool enough for electrons to be bound to atomic-- To nuclei.  And so you have atoms formed. 

 And once that's true, then suddenly the universe becomes pretty much transparent.  And so this is a period when before star formation has really started, and there's gas that becomes atomic.  And, as a consequence, you have a dark universe.  Okay, and so it's called the Dark Ages.  And this is a change from a radiation to a matter dominated universe.  Up until this time, the largest number of particles in the universe was photons and neutrinos.  Since neutrinos don't interact, we're not going to say much more about them here.  But, at this point, when you start to form atoms, matter takes over as the dominant form of particles in the universe.  Okay, now we go to about a billion years.  This is a period of star galaxy formation. 

 Temperature has now dropped to about 70 Kelvin or about minus 200 degrees Centigrade.  Gravity has gathered matter into filaments and massive clouds that give rise to the formation of the first stars and galaxies.  And that's at an age of about a billion years.  At this time, it becomes possible for carbon based life forms to appear in the universe for the first time.   About nine billion years ago, the solar system is formed in the Milky Way.  And from about one to nine billion years it's possible that life could have emerged many places in the universe.  Life on Earth arose at the age of about 10 billion years.  About 500 million years after Earth's formation.   But this would have undoubtedly been prokaryotic lifeforms, not the lifeforms like we're made out of, but more primitive lifeforms.  The eukaryotic lifeforms didn't appear for another two billion years or so. 

 Okay, current age of the universe is about 13.8 billion years, and the current temperature of the universe is 2.73 degrees.   And I don't think I need to say any more about this.  This is what I was trying to talk about a while ago, though.  Time versus temperature.  And the density of radiation is going down at a steeper rate than the density of matter.  And you see there's a crossing point here, and that's when you convert from a radiation-dominated universe to a matter-dominated universe.  The big T here is just the change in temperature with time.  And that's determined entirely by the cooling due to expansion.  Okay, now I'm going to do something that I should never do in a general audience.  I'm going to write an equation down; it's a fairly complicated one. 

 But I'm going to tell you-- Try to explain what's going on here.  This is a relationship that was derived by Alexander Friedmann, who was a Russian meteorologist who taught himself relativity theory and then started working on cosmology and wrote this very beautiful equation.  It's called the Friedmann equation and basically what it is is what's call an equation of motion of the universe.  And so this H-naught we've already talked about, and the H sub T squared is the Hubble constant at any other given time in any other time.  Remember, it is a function of time.  The universe is not expanding uniformly.  It's slowing down, or at least we thought this up to a few years ago.  Okay, so that is determined by the sum of the omegas.  Omega R, omega radiation, omega mass, and the dark energy, omega lambda.  But it has this dependence on this A factor. 

 The A factor is what's called the scale factor of the universe.  And basically all it is is the average separation on a cosmic scale of clusters of galaxies.  So the average separation of clusters of galaxies, of course, is getting larger as time goes along.  So that's a function of time.  It's just basically just determined by the expansion of the universe.  And you can see that the radiation term here goes as this scale factor to the fourth power in the denominator.  And so it decreases very fast in its importance in the motion of the universe.  Similarly, for mass, omega M here is divided by A to the third power.  And so it decreases very fast too.  Not as fast as radiation, but as we saw, the universe did convert from a matter-dominated to-- to a radiation-dominated to a matter dominated universe. 

 That's because of that dependence on A here.  Omega lambda doesn't depend on A at all.  As a consequence, at some point it becomes the dominant factor in the evolution of the universe.  And this one minus omega naught-- Omega naught is the sum of the other three here.  So we're making the assumption that we know everything that's in the universe is either photons, matter, or dark energy.  Well, we think we've determined what these three quantities here are.  And so omega, we believe, is one.  And so that's the term that determines the geometry of the universe.  And if omega is one, that last term goes to zero, and that tells us that we live in a Euclidean universe.  The universe is flat in that sense. 

  Okay, I'm going to-- This cosmic scale factor, I've already said what that is.  You can convert this to a much simpler kind of expression.  Whereas this is the rate of increase of the scale factor.  So it's a speed.  And you can see it depends, when you write it this way, you still see the dependence on A and this-- When you write it this way, you see that omega lambda is multiplied by A squared.  The others have A in the denominator, so they go down rather fast.  Okay, well, anyway, that tells us, though, that omega lambda is going to become, and in fact is now, the dominant player in the evolution of the universe.   Okay, I'm going to kind of skip some of this because I don't want to-- I want to tell you what the present, what's called the standard model of the universe is today from all the best measurements we've been able to make.  The current temperature of the universe is 2.725 plus or minus 0.001 Kelvin.  H-naught is 67.3 kilometers per second for every three million light years distance, increase in distance. 

 And the age of the universe, as I say, is about 13.8 billion years.  And Q-naught is less than zero, and we're going to see that that tells us that the universe is not slowing down.  It's actually accelerating in its expansion because lambda, the omega lambda is the dominant term now, and it behaves, in a sense, like antigravity, if you wish.   So the amount-- the radiation term here total is only eight times 10 to the minus five.  This is a ratio remember.  It's the fraction of energy density that's in the form of radiation.  And that is almost-- It's not much.  10 to the minus five, 10 to the minus four.  In photons, is five times 10 to the minus five.  And in neutrinos, it's three times 10 to the minus five. 

 The sum gives you 8.4.  So, photons are not contributing very much at the moment to the evolution of the universe.  Matter has a value of about 0.315, and of that, baryons only contribute about 5%.  Baryons are the stuff we're made out of.  It's the stuff stars are made out of.  Galaxies are made out of. It's us.  And so most of what we know about the universe is only determined by about 5% of the contents of the universe.  Okay? So that right away should bring some red lights to your head.  The dark matter, omega dark matter, is also part of the matter.  And it makes up almost 27%. 

 So, the stuff that we call dark matter, we don't know what it is.  It's 27% of the contents of the universe.  Omega lambda, the dark energy, is almost 70% of the universe.   And since-- If you sum these up, you get about one.  So that means omega naught is one, and, consequently, the geometry of the universe is what we call a flat universe or a Euclidean geometry.  Now, be aware that we're assuming that we've included all the content.  That we know what all the contents of the universe is.  And that ain't necessarily so, possibly.  It's an uncertainty.  I'm just going to show you this. It's kind of complicated. 

 I'm going to just zip over it.  So I'm going to give you a thumbnail picture of the evolution of the universe, starting at the big bang right here, which I didn't say anything about because we don't know anything about it.   But we had this inflation period where the universe just explosively expanded by maybe 25 orders of magnitude in a tiny, tiny fraction of a second.  And then we had the formation of protons.  And then we had nuclear fusion at these various ages.   Time is running along on the bottom here.  And think of the size of the universe, if you wish, as the height.   Okay, well, in any case, this is kind of a thumbnail picture of what we've been talking about.  And let's just now ask about the future.  And there were four possibilities. 

 If you think about the present as right here.  When I was a grad student, we used to argue about whether the universe, although we knew that it's expanding now, its own gravity may have been enough density of matter, it was possibly large enough that it could actually collapse on itself and go back into a singularity.   Other possibility what's called a critical universe, where it's expanding outward as it goes, but it's never-- There's never large enough density of matter to actually cause it either to come completely to a stop or certainly not fall on itself.  And then a coasting universe where it just continues out uniformly expanding.  And the one that now seems to be the best assumption is the accelerating universe here because dark energy has taken over and the universe is actually accelerating at today's, at the present time.  So that's the one that the standard model now predicts.  But there are many questions.  How much might we be missing by only observing 5% of the contents of the universe? Might there be other undiscovered constituents? That is, is omega not equal to one as a current standard model would predict? What is dark matter? We don't really know what that is.  What is dark energy? We also, you know-- Why does dark energy behave like antigravity? Why is dark energy independent of the universal scale factor? As everything else, all other constituents in the universe depends on the scale factor but omega lambda does not.  And that has to go back to the mathematics of when Einstein introduced this lambda term. 

 And he introduced it because the Friedmann equation was unstable.  So, anyway, he thought it was his greatest error, but it almost certainly was not.  If neutrinos have mass, as experiments seem to imply, why have antineutrinos not disappeared from the universe? Another good question.  What triggered the inflation of the universe, and what stopped it? We know basically essentially nothing about the Planck period and the laws of nature that govern the interaction of particles at this very earliest stage, and we probably are not going to know much more about it until we understand the quantum nature of gravity.  Gravity is the one force that we still, believe it or not, it sounds simple but it ain't, believe me.  It's a very complicated issue, and we don't know how it would behave in a quantum sense.  And so that's still a big open question.  Fundamentally, why is the universe expanding? Okay, well, I should stop there.  I think I've taken plenty of time.  So, thank you very much. 

 I would be glad to take questions.  [applause]