Frontiers and Controversies in Astrophysics

ASTR 160 - Lecture 21 - Dark Energy and the Accelerating Universe and the Big Rip

Chapter 1. Review of Dark Matter [00:00:00]

Professor Charles Bailyn: Welcome to prefrosh [newly admitted students visiting during Yale's "Bulldog Days" program]. I'm talking about black holes at 8 o'clock this evening. Come listen to that, too, and in the meantime, we'll talk about the future of the Universe. Okay. Logistical questions? Anything?

All right. Where were we? We were here. This is the data that demonstrate that the Universe is filled with dark energy, a kind of anti-gravity that is pushing the Universe apart. And what this is--this is the same data on both of these plots, just plotted slightly differently. On the top plot, what they've done is they've plotted the apparent magnitude of these supernovae versus their redshift. And so, apparent magnitude--because the absolute magnitude is always the same. These are standard candles. So, from the apparent magnitude, you can figure out what the distance modulus is. That gives you a measure of the distance. So, this is just distance versus velocity.

Now, we've plotted distance versus velocity of bunch of times. That's the Hubble Diagram. Most of the times we've plotted it, it's come out on a straight line. Do you understand why this plot isn't on a straight line? The top one, I'm talking about, now--why those lines are curved? What's the y-axis? The y-axis is--yes?

Student: It's logarithmic.

Professor Charles Bailyn: It's logarithmic. Thank you very much. Yes, it's magnitude. Magnitudes are upside down and logarithmic, right? That's why faint stars have high numbers up at the top. And because one axis is logarithmic and the other axis isn't, of course, it curves. You could--the way--if you want a nice straight line, you just make this axis logarithmic, as well.

What we've done down on the bottom is just subtracted off the empty Universe--a Universe with no matter and no energy in it--so that you can see more clearly the way these three lines diverge. And these three lines are three different models of the Universe. And they're denoted by these Ω factors. Ω matter, that's the density of matter divided by the critical density. Ωλ, that's the energy density of the dark energy divided by that same critical density.

And down here is an Ω matter of 1. That's the dividing line between a Universe that re-collapses and a Universe that expands forever. So, if the Universe were--if the points that we studied were down here, the Universe would re-collapse. If they're up here, it wouldn't. This dotted line here is ¼ and 0.

¼ in Ωmatter is the amount of matter that we actually observe in dark matter and galaxies. If you go out and count up all the dark matter in the galaxies, add it all up, you get to about ¼ of the critical density. So, what people were kind of expecting to see was something between here and here.

And, of course, that wasn't what happened, as we discussed last time. Turns out, all the points are too high, and therefore, you end with a current best fit--the best guess for the way of the Universe is this solid line here. This is called the standard model or the concordance model, where you've got a ¼ of--the Ωmatter is ¼, but there's a whole bunch of dark energy. ¾ of the Universe is in this mysterious form of dark energy, which tends to push things apart rather than pull them together. That's why these points are above the 0 line, instead of below it. And that's the current best idea for what the Universe is.

So, by virtue of the fact that these points lie on the solid line rather than on somewhere between these two dotted lines, or perhaps even below, we make this remarkable conclusion: that the Universe is ¾ full of something we absolutely don't understand, called dark energy, which has the effect of an anti-gravity. And then, it turns out that Einstein's biggest mistake is right after all.

Pretty hefty conclusion to lay on the basis of two dozen points with, let it be said, pretty sizeable error bars on any one of those points. And so, I thought, at the start of today, I would talk about what these points are, how they are measured, and what could go wrong with this kind of measurement. Because, you know, we've transformed what we think about the Universe based on this. And so, it behooves one to actually try and understand what's going on. I'll come back to that in a minute.

Chapter 2. Supernovae [00:04:51]

So, what are these points? What are we measuring? And why do we think it might even work? What we are measuring is Type Ia Supernovae. So, this is typically astronomical nomenclature, right? We go out. We find a bunch of things. We divide them into categories. We call them Type I, Type 2. It then turns out that each of those categories has sub-categories, Type Ia. The joke is when astronomers find three objects, that's two categories and an exception. Type IaSupernovae, though, are by now a fairly well-defined category, and here's what we think they are.

Think back to the middle part of the class--to the black hole section of the class, where we were talking about x-ray binaries. X-ray binary, you'll recall, is a black hole in orbit around something--some other kind of star, and it pulls material from that other star onto itself. So, Type I Supernovae come from a very similar category of objects.

Here's a normal star, except it's pulled out of shape a little bit, and it's in a double star system. Here's something else. This is a white dwarf. In this case, you will remember, white dwarfs are these very compact stars--not compact enough to be black holes, but fairly compact--that are created at the end of the lifetime of stars like the Sun. So, a fairly dense object. And just as in the x-ray binaries, stuff is being pulled off of the normal star onto the white dwarf.

So, then, what happens to this stuff? First of all, the white dwarf has had all its hydrogen and helium fused together, so there's no hydrogen or helium left. So, this white dwarf is composed of elements like carbon and oxygen and nitrogen and neon, and so on, up the line, but no hydrogen and helium. So, the material that comes from the normal stars, full of hydrogen and helium--it's pretty much all hydrogen and helium.

So, the accreted material, what does it do? Lands on the white dwarf. And as it lands, it heats up. It falls down. It heats up, gets very hot, gets very dense. And so, it undergoes nuclear fusion, just like the material in the middle of the Sun or in the middle, presumably, of this normal star, as well.

So, there's all this fusion going on. One of the features of the way this works on a white dwarf is it is usually true that what happens is hydrogen and helium piles up for a while, and then, it has a big explosion. It doesn't usually burn steadily.

And so, what actually happens is, you have occasional thermonuclear explosions of the accreted material. And so, you pile up all this hydrogen and you wait some amount of time, somewhere between 10 days and 105 years, depending on the object. You pile up all this hydrogen and helium and finally it gets dense and hot enough to explode, and then it explodes all at once. Huge hydrogen bomb on the surface of this white dwarf. And that makes the system much, much brighter, because there's all this stuff exploding. This is the phenomenon we call a nova, because it looked to the ancients as if a new star had appeared, because the thing had gotten so much brighter.

Okay. So, stuff piles up. Novae occur. More stuff piles up. More novae occur. And one of the things that's happening while this is going on is that the white dwarf is gradually getting more massive, because it's piling up all this extra material.

Oh, the consequence of the nova is that all the hydrogen and helium gets fused into carbon, oxygen, nitrogen, neon, and so forth. So then, it looks just like the rest of the white dwarf, gets assimilated into the white dwarf, except the white dwarf is bigger now.

So, the white dwarf gets more massive and gradually more, and more, and more massive. But, you may recall, there's a limit to how this long could go on. The reason there's a limit to how long this can go on is because of something we talked about before that Chandrasekhar Limit, which says that white dwarfs cannot be more massive than 1.4 times the mass of the Sun. So, what happens when this white dwarf, which starts out at some perfectly respectable mass, 0. 6 of the Sun, or 1 solar mass. And it's piling up all this material from its friend, and gradually getting more and more massive, and then, it reaches this limit, this Chandrasekhar limit. So then, what happens?

What happens--remember what the Chandrasekhar limit is. If you've got a white dwarf that's bigger than the Chandrasekhar limit, then the white dwarf cannot hold itself up against gravity, and so, the whole thing collapses all at once. And, as is generally the case, when it collapses, it gets hot. It gets dense. That's what generally happens in a collapse. And so, the carbon, in particular, but all the other elements as well--so, carbon and other elements in the white dwarf fuse, and that generates energy. And they fuse together to form heavy elements such as iron, and heavier than that, all at once.

So what happens is, every time this occurs, you have exactly the same amount of stuff. This always happens when you have 1.4 solar mass white dwarfs, because that's the limit. You've gradually built up to that limit. And so, you have what you might refer to as a standard bomb. We've talked about standard candles. This is a standard bomb. You always have the same amount of material and it all explodes at once. Well, actually, it takes about, what? A hundred milliseconds, something like that, but basically, all at once.

So, you blow up 1.4 solar masses of carbon all at once. Now, the advantage of standard things is that if you have a standard bomb with the same amount of fuel, every one of them should be exactly as bright as every other one, and that's what we need to make these distance measurements. Remember? So, if you look at these things, you see that they're always the same brightness, so, they're terrific standard candles.

And so, one of the things that happens is that you look at these things and you can tell, from how bright they look, exactly how far away they are. You also measure their redshift when they blow up in this way, and you get to put a point on that redshift versus distance plot. And they're stupendously bright. These things have an absolute magnitude of -19.5. They outshine whole galaxies, for about a week or two, until they go away. And so, you can see them at enormous distances. So, they're just about the perfect thing for exploring cosmology.

But we were only really able to do this in the--starting in the early 1990s, because there were two key advances that were made at that time. One is that the Hubble Space Telescope measured things like Cepheids and other kinds of stars, other kinds of distance measurements, in galaxies that historically had Type Ia Supernovae. These things don't occur very often, once every couple of 100 years per galaxy. There hasn't been one in our own galaxy since before they invented the telescope. We're kind of overdue, actually. One of the worrying things‒

You know, it would be great to have one of these supernovae in our galaxy. We could study it enormously carefully. The problem is, all the telescopes are too big and--because it would burn out all the instruments. You put one of these big research telescopes pointing to it. So, one of the things that we have, just in case, sort of, for emergencies in the telescopes I've worked with in Chile, is we have a big thing you can put over the front of the telescope and stop it down to about a couple of inches across, just in case there's a Type Ia super--any kind of supernovae in our own galaxy.

But when these--we do have supernovae in the historical record. Kepler and Tycho saw one. And then, back in the eleventh century, there was a famous one observed by the Chinese and Arab astronomers. The Europeans were, of course, in barbarity at the time and didn't even notice. And--which, now, we see the Crab Nebula, which is a big outward-going explosion. And these things become the brightest objects in the sky. You can see them in the daytime. Pretty amazing, but it hasn't happened for 400 years, at least, in our own galaxy.

Student: How long did you say they lasted?

Professor Charles Bailyn: They last--well, I'll show you in a minute what the light curve looks like. They take a couple weeks to rise to their maximum brightness, and then they decay over a few months. So, you can see them for a little while.

So, it just--measured Cepheids. This meant that we could calibrate them. Remember the distance ladder? So, you could calibrate these things ‒ calibration. And this, in particular, meant that we know the absolute magnitude, which is crucial for determining these distances.

What, then, came out of that and other things, mostly, actually, done with ground-based telescopes--so, ground-based telescopes discovered and compared many of these things, many of these Type Ias, and discovered that, you know, it isn't actually quite true that they all look to be the same brightness. Because, it would be true, if you could measure all of the energy that came out of these things. But that isn't actually what you measure. What you measure is all of the photons in a certain range--depending on your detector and how you set your telescope up--all photons within a certain range of wavelengths at a certain time. And that is not the same thing as measuring all the energy that the thing gives out.

And so, it turns out that if you measure all photons in some wavelength region at some time, that actually varies from one object to another. This can vary by, oh, I don't know, 15 - 20%, but that's enough to cause you some real trouble in making these measurements. But what they discovered was that you can correct for this. If you measure the color and the decay rate--that is to say, how fast it gets fainter. So, your question turns out to be very important. These things behave differently depending on how fast they go away. If you measure the color and the decay rate, you can correct for some of these deviations and turn it back it into a good standard candle. And I'll show you how this is done in just a second, okay?

How we doing? Okay, let me turn this off for a second and go back to here. All right. This is the key thing that was found out in the early 1990s. Up on the top, you have observations from a whole bunch of supernovae. This is time. So, this is 0, 20 days, 40 days, 60 days. So, this is time, counting from the peak brightness. And most of the time you can observe these things before they get to peak brightness. You watch them get brighter and then you watch them get fainter. In the top plot there, we're plotting, more or less, absolute magnitude. Think of it--it's a complicated thing, but think of it as absolute magnitude. So -19.5, as I said, is a typical magnitude--absolute magnitude. And each color is a different supernova. So, they've made repeated observations of a large number of supernovae. And then, the line is just connecting the dots, connecting the observations.

And you can see from that top plot that it is not true, that every supernova has the same brightness, at peak or at any other time. And so, the green supernova on the bottom there gets up to about -18.8, whereas, the orange one on the top gets up to about -20. That's almost a factor of 3 in difference of peak brightness.

But then you can make this correction. They measure the color of the thing, which is not apparent on this particular plot. They measure the rate of decay, and that is apparent. You can tell the green ones, the ones at the bottom, tend to fall off faster than the ones at the top. And they came up with a correction formula that allows the absolute magnitudes of these things to be corrected, and that's what they plot here. These are these same exact data points as they have on the top line, except corrected for the differences in observed color and observed decay rate.

And you can see, now, you've got a very beautiful combined light curve where everything does exactly the same thing as all the others. And, in particular, the maximum brightness of these things is always the same at around -19.5. So, you have to make this correction in order to be able to use these things effectively as standard candles.

And so, when that was done, and we had calibrated this, and they thought, well, now we know, every time we see one of these things, we'll just follow it up, follow it down, make this correction, and then we have--we know what the absolute magnitude is. We measure the apparent magnitude. We determine the distance. We get a spectrum along the way so that we can get a redshift. And then, we can make these plots for distant objects. These guys aren't particularly distant, because you want to be able to get really accurate measurements of them. And so, if this set were the ones that were observed so close to us at such low redshifts that you can't tell the different cosmological models apart.

Chapter 3. Finding Supernovae: The Supernovae Cosmology Project [00:20:53]

So then, people got very fired up. They said, aha, we're going to figure out everything that is happening in the Universe by looking at these supernovae. And they started up big observational projects to find many high redshift supernovae. So, these things are going to be quite faint. They're going to be--they have distance moduluses of close to 45, and so, they'll have an apparent magnitude as low as 25, which is really very hard to see.

So here's what they do. First of all, let me just show you this picture. This is just fun. Let's see, here. If I do this, that will be good, except I think I want this. There we go--all right. This is a photograph from the Hubble Space Telescope of empty space. They picked a part of the sky in which there was nothing. Actually, that's not true. There was one star, one faint star that they knew about, and nothing else. And they took the space telescope and they looked at it for about three weeks in a row. And this is the picture they got.

You can see two or three stars in this picture. This is one, and there are a couple of others scattered around. You can tell they're stars because they have this, sort of, spike pattern from the optics of the telescope. Everything else that you see in this picture is a galaxy. There's a whole galaxy, each one of them with billions of stars. There are, I think, 13,000 of them? 8,000? How many in the ultra deep field? I don't remember. Huh?

Student: Are any of them lensed?

Professor Charles Bailyn: A couple of them are lensed, but most of them, not. So, most of them are just straight-up images of galaxies. You could see, in the bigger ones, some nice spirals and all the usual kinds of galaxy shapes.

This is a really small piece of the sky. This is a piece of the sky about 1% of the area of the full Moon. So, if you looked at the whole area covered by the full Moon--picture the full Moon up in the sky--and you did this kind of picture, you would discover literally millions of different galaxies.

So, this means that you can discover supernovae in the--so, there are thousands of galaxies, here. And if supernovae occur once per every 100 years per galaxy, there ought to be about ten or twenty supernovae going off in this tiny piece of space right now. Or any other such tiny piece of space. And so, if you're looking for high redshift supernovae, you don't care where you point. They're everywhere. And so, you just pick out some nice blank piece of space, take really deep pictures of them, and wait for the supernovae to start showing up. And this is what people have done.

So, here's a little bit of data from the Supernova Cosmology Project, which is one of the groups that was attempting to do this in the 1990s. So, in the background, here, is just a huge field of stars that they happened to be looking at. Then, they've taken this tiny piece of the sky and blown it up. So, here's their first image of it. By the way, this, and this, and this--these are galaxies, but they're taken from the ground instead of with the space telescope. And so, they look like blobby things. You can't see any of the structure.

And then, three weeks later they take another picture, and it turns out, there's a little extra light on the side of one of the galaxies. Now, imagine taking something maybe 100 times bigger than this whole background picture and looking for that difference. You would make your graduate students completely cross-eyed doing this. And so, they do it digitally. They do it differently.

What you do is you take this picture, each one of these pixels, you know, tells you exactly how many photons hit it. So, it's all digitized. Each one of these is a number. And you just take this number and subtract this number. And you take the number from each pixel, subtract the number that you got in the previous thing and get a subtracted image of how much light there is, minus the light there was the last time you looked at it.

Here's the subtracted picture. Now this, even a blind old professor can see, has something interesting going on. There's a new object that has appeared between the first picture and the second picture. Now, up at the top, in the upper right-hand corner there, that's a Hubble Space Telescope picture taken of the same field, while the supernova was in outburst. And you can see, this galaxy, here. That's the galaxy, you know, below the arrow there. And then, those two arrows are placed in exactly the same relative position in these two pictures.

And so, in the Hubble Space Telescope picture, you can see that the additional light comes from a particular point in the outskirts of the galaxy. But it wasn't discovered with the Hubble Space Telescope, because the HST doesn't cover enough of the sky at once. So, you try and discover these things from the ground, because you can cover so much more of the sky. And so, this is a discovery image. And then, if you want more precise imaging, then you have to tell Hubble, or go and look at this particular place.

Anyway, what they do is they keep at it. They keep at it. Every three days, they make one of these pictures. They make these difference pictures, and they get these nice light curves. And out of those light curves, they can then do the correction factor. And then, once you've done that--you also take a spectrum along the way for two purposes: first of all, to get the redshift; second of all, to make sure that it's a Type Ia Supernova, rather than any of the other five or six subtypes. And then, you put them on this plot and you plot their apparent magnitude, corrected by these various factors, against the redshift. And that's how you come up with these kinds of data.

So, that's where this information comes from. And there is, as you see, a kind of theoretical--both a theoretical reason and an observational reason to trust these results. So, there is a theoretical basis for thinking these things are standard candles--namely, that it's the same amount of fuel each time one of these things goes off. And there's also an empirical basis, which is that after some corrections, the nearby ones line up beautifully. The nearby ones, for which you know the answer in advance by other means--the nearby ones line up well. And where by "well", I mean less than 5% difference between them. And there still is about a few percent difference. But if we observe enough of them, we can average over that and we think we're going to be okay.

So, if you want to come up with some kind of explanation for this that does not involve dark energy, you've got to get around both of these points; namely, the fact that we expect them to look like each other, and the fact that they do look like each other. Now, it's possible to do that and, in fact, one of the problems on the problem set addresses just this issue. If you can invent some way that all of the supernovae at a redshift of .8, high redshifts like that, are all systematically fainter than otherwise identical-looking supernovae in the nearby Universe, then you can get around this problem. But they have to be identical-looking in the sense that they have the same color and decay rate, but are fainter.

We don't see that in the local Universe. We don't see a category of things, which have the same color and decay rate, but one is fainter than the other. But, who knows? The Universe was, you know, half its size back then. All sorts of things were different. Maybe there's some way that supernovae then were systematically different from how they are now, except that they don't show it in these particular ways. They only show it in the overall brightness. That's tough. That's tough, theoretically. It's tough empirically. You know, you would expect that if that were true, then there would be intermediate cases that we could see, and we don't see them.

But, you know, shortly after this result was announced, I used to--when I was at conferences and stuff, I would try and take the supernovae people off in a corner and give them beer and stuff, until they would, you know--and then, after you give them four beers, you ask the question, what could be going wrong? Do you really believe in dark energy? And then, they start mumbling stuff about all the different weirdnesses that supernovae have. And, of course, these are people who have devoted their life to studying the weirdness of supernovae, and so, they have many things that they will tell you under cover of darkness. Which, of course, then, everybody went out to try and check. And none of these things have turned out to be able to provide a satisfactory explanation for the data, except the idea that there's something very significant, cosmologically, going on.

Okay, so, from that point of view, it's kind of hard to avoid believing this, which disturbed a lot of people. And, in fact, one of the reasons people believed this as quickly as they did was that in the late--in 1998, when this was first announced, it was not announced by one group, it was announced by two different groups. There were two groups trying to do the same thing--doing the same thing and theyso, they were sort of spying on each other, because this was an important result. And they both found out, at a certain point, that the other guys had been spending a year driving themselves crazy because they didn't believe their results. They were saying, look at this, these things are getting--these things are going totally in the wrong direction. We must be wrong somehow. And it turned out that both of these groups had been spending the past year trying to figure out why their results were so screwed up. But then, they spied on each other and they found out that the other guys were having the exact same problem, having taken their data and dealt with it in quite a different way.

And so, then, miraculously enough, they kind of submitted their papers within twenty-four hours of each other, so they both got credit. And so, the two groups doing the same things, but doing them differently. Different approaches, in some ways, got the same result.

And in particular, one group were a bunch of particle physicists led by Saul Perlmutter, who had gotten depressed by the fact that the Super Collider was cancelled in the early 1990s, and had decided--somebody described this as "adult onset cosmology," where you used to be interested in particle physics, but then, they didn't build your machine, so now you're interested in astrophysics. And those guys took a very particle physics approach to it. They had a big team, with a team leader and a whole hierarchy. The other guys were a bunch of supernova--and they were very expert in the cosmology side of things, and in the dark energy explanations, and stuff like that.

The supernova experts, the sort of guys who knew all the weirdnesses about supernovae, formed another group, but it was totally differently organized. It was kind of a loose confederation of small research groups here and there. They had done this interesting work with the correction factors on supernovae some years before, and they approached it as, you know, my group will do this little piece. My group will do this other little piece. We'll get together over lunch and we'll figure out what's going on, kind of thing. And they both got the same kinds of answers. They both basically got the same answers.

And so, this is one of the fables. So, fable: discovery of dark energy. And I would say that the moral here is that replicating important results is one of the things that leads people to actually believe what you're saying--leads to greater acceptance.

And it was particularly nice in this particular case, because neither of them were replicating the others. They both made the discovery independently, at the same time, using a very different kind of organizational structure and a very different approach to their data. So, this was kind of compelling.

Chapter 4. The Constant Density of Dark Matter and the Big Rip [00:34:41]

Okay. So, here we are, Δ (m ‒ M), versus redshift. Here's Ω matter = 0.

Ωλ = 0, except that, in fact, the data--you know, they kind of look like this. So, this is Ω matter = ¼ and Ωλ = ¾.

And, as you will recall, the explanation for this--or, the first explanation that was offered was the fact that Einstein had this figured out eighty years before, except he decided he was wrong. And so, the first explanation of this was Einstein's Cosmological Constant--that's this symbol, lambda [λ], that I keep writing down.

And so, once people believed this result, you had to start worrying about what the heck this actually is in real life. And it has some very peculiar properties. In particular, there is the issue of what is constant about Einstein's Cosmological Constant?

So, let me first tell you what it is, and then, I'll tell you why it's so bizarre. The energy density ‒ remember, that's the crucial quantity--of λ is constant as the Universe expands. So, if you take 1 cubic meter of space, and you say, how much dark energy is there in this cubic meter of space? We take an average cubic meter of space. You figure that out by how fast the Universe is being pushed apart. And then, you know, you wait 10 billion years, or something like that, until the Universe is very much bigger. And then, you take a cubic meter of space, and you ask yourself how much dark energy is in this cubic meter, and you get the same answer, 10 billion years later. And you got the same answer now, and you would have gotten the same answer 10 billion years ago.

Very peculiar, right? Do you see why? Think about matter. You know, the Universe also has a bunch of matter in it. All right, so I measure the average density of the Universe in the way we've discussed, and you get some answer. So, for matter, you can get some density to the Universe now. And then, supposing you imagine in your mind, you go back in time when--to the time when the scale factor of the Universe, when a was half its present size, its present amount. But, of course, you have the same amount of matter in the Universe. Matter doesn't--you know, in general, it doesn't get created. Or, at least, you have the same amount of matter plus energy. So, you go back to when you have the same amount of matter, but it's in half the size, by which I mean, the volume, right? Half squared--half cubed is . And so, if I reduce the linear scale of the Universe by a factor of two, I have the volume, but same amount of matter.

So rhothen, which is equal to mass, which doesn't change, because there's the same amount of mass in the Universe, which doesn't change, divided by volume, which does change. So, it has to equal eight times the densitynow.

We've talked about this before, right? The whole deal with the Big Bang is that if you go back into the past, things were denser than they were today. Also hotter, which is a by-product of the density. You take a big balloon full of stuff. You make it smaller. The same amount of stuff is in there. It's got to be denser inside the balloon after you've squashed it down. You take a balloon and you stretch it out. If you don't let stuff come in or out, then it has to be less dense--the stuff inside, after you've stretched it out. And then, you get into all these nice little thermodynamics problems where you have, pressure is equal to density times temperature, and things like that. So, all of familiar gas physics comes into play.

And so, you expect that the density of the Universe is constantly getting smaller, because the Universe is getting bigger. And, in fact, there's extremely good empirical evidence of that, because you look back in time by looking at distant things. Sure enough, it's denser back then.

But not the dark energy. Dark energy density, at least in Einstein's conception, is constant. So, a cubic meter of the Universe has the same amount of dark energy in it now as a cubic meter of the Universe did when the Universe was only a cubic meter across, right? Where the whole observable Universe was packed down into a cubic meter, that cubic meter had only as much dark energy in it as, you know, this part of the Universe does now. Very odd behavior, but this is what Einstein's equations predict.

Now, the thing is, we don't know that Einstein really was right. We don't, because we don't have a clue what the dark energy actually is. So let me--so, λ, the Cosmological Constant, suggests that dark energy has constant density. But, since we don't know what the heck this stuff is, maybe that's wrong.

Or maybe not. If it's not, we don't call it λ anymore. But if you allow for changes in the density, you can get very interesting potential effects. And let me--we'll talk about this more next time, but let me just describe one of the very strange things that could happen.

Suppose it is true--and this is not ruled out by the data we have so far. Suppose the dark energy density increases as the Universe gets bigger. And since we don't have any idea what this stuff is, it might do that, and we can't rule it out by observations just yet. And so, the Universe gets bigger and bigger. The density of the matter is going down, because you have the same amount of matter in a bigger space.

But, supposing we invent some kind of dark energy where the density actually gets bigger as the Universe increases in size. Then, a cubic meter of volume has increasing dark energy as time goes along. That, of course, pushes the Universe out faster, so the acceleration increases. That makes the size increase and you get a feedback as the Universe exponentially expands. You get an exponential expansion. And as that exponential expansion increases, the amount of dark energy in any particular cubic meter gets bigger too.

And so, what happens? After a while, the dark energy in any cubic galaxy has become so much that it blows the galaxy apart. Gravity can't hold the galaxy together. And then, the expansion continues. And then, after a while, the amount of dark energy in one cubic star, if I can use that term, in one star becomes so great that it overcomes the gravity of the star and it blows the star apart. And then, the expansion continues even faster. And after a while, the amount of dark energy in a cubic meter--that would be a human being. Remember, human beings are exactly a cubic meter and exactly 100 kilograms in mass. The amount of dark energy in a human being overcomes the chemical bonds that hold your body together and human beings get blown apart. And eventually, you have so much dark matter that whole atoms--that atoms get blown to bits, and even the sub-atomic particles that are within them eventually get blown to bits. And so, dark energy conquers all.

This is described as the Big Rip, and it is kind of an alternative hypothesis of what might happen to the Universe, that stems from an alternative hypothesis of what the dark energy is, that there's no particular reason to believe, but that hasn't been disproved. And since there's no particular reason to believe anything else, you can amuse your students by talking about it.

So, to summarize this, here is--it's all a question of the scale factor versus time. Here is now. Here is 1. Here is an empty Universe. We thought that what would happen is that it would look like this, and either collapse, or not. What actually happened is, it turns out, things look like this. We only really observe it in the past, so there's a whole bunch of supernovae proving that that's true. And you can extrapolate a kind of gentle expansion that looks like this. This is the standard model with a Cosmological Constant. But if you assume that things get even bigger--that the dark energy increases per volume with time, then you asymptotically go to infinity at some time in the future and you blow everything apart.

Not ruled out. And so, people are anxious to discover whether that, or some other set of crazy ideas, might be true. And we'll talk about how people are going about trying to nail this down next time.

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