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Professor Charles Bailyn: We've been talking about the Type Ia Supernovae and the data that they provide about the expansion and, as it turns out, acceleration of the Universe. And so, one way to summarize all that information is that what we have found out — we now know that the Universe is accelerating, not just expanding, but accelerating. And that acceleration comes about because of some kind of dark energy — or to turn it around, the label we give to whatever is calling that is dark energy. And this sometimes gets summarized by this quantity, which is the energy density of the dark energy relative to the critical density of the Universe. And the fact that it's accelerating means that this quantity must be greater than this other quantity, the density of matter, because the matter tends to pull things together.

And so, we know not only that it's accelerating, we know something about how much it is accelerating, and that tells us how much bigger the dark energy density is than the matter density. And we kind of know by how much. We kind of know how much bigger this is than the dark matter density.

But somebody actually asked the question that, you know, I keep saying, well, this is like 3/4, and this is like 1/4. If you add a bunch of matter, couldn't you just add a bunch of dark energy also, and end up with the same amount of acceleration? So, a comparable Universe. And the answer is, yes, you could. There's nothing in the supernova data that prohibits this from being .5 and this from being 1, as long as this is sufficiently greater than that by the amount necessary to give rise to the observed acceleration.

And so, if you plot these two quantities against each other — so, here's, kind of, 0, 0. Actually, this can be negative, but let's not go there.

1, 1. What you find out is that there's a kind of allowed region that sort of looks like this, allowed by the supernova data. Notice, this is — I'm assuming throughout that the dark energy really is the Cosmological Constant. I'm not thinking about Big Rip scenarios at the moment, because that would add a third dimension to this plot, and I don't want to do that just yet. So, this is all assuming that dark energy is the Cosmological Constant. But that's certainly a place to start. There's no reason not to do that.

And so, I've been kind of consistently claiming, as we've been talking about the course, that the real answer is somewhere like here. Yeah? That it's about .3 on the matter side, .25 and about 3/4, 2/3, 3/4 on the dark energy side. But, in fact, you could go — as far as the supernova care, you could have no matter at all and just a little dark energy, or you could have a lot of matter and a huge amount of dark energy. And you'd get the amount of acceleration, and therefore, satisfy the observational constraints.

But, in fact, it turns out, we know more than this, because there are other constraints on cosmology besides the supernovae. And, I have to tell you at this point that this course, the way I've presented it, is a little bit lopsided, because the other ways of constraining these two quantities are just as important as the supernovae, and I'm going to do them all in one lecture. And this is kind of in the spirit of the philosophy of this course, where we try and understand a few things in depth, rather than many things in breadth. But I'm going to talk about two other kinds of constraints on cosmology today, which are, in fact, just as important to modern cosmology as the supernovae are.

And so, we know not only that it's accelerating, we know something about how much it is accelerating, and that tells us how much bigger the dark energy density is than the matter density. And we kind of know by how much. We kind of know how much bigger this is than the dark matter density.

But somebody actually asked the question that, you know, I keep saying, well, this is like 3/4, and this is like 1/4. If you add a bunch of matter, couldn't you just add a bunch of dark energy also, and end up with the same amount of acceleration? So, a comparable Universe. And the answer is, yes, you could. There's nothing in the supernova data that prohibits this from being .5 and this from being 1, as long as this is sufficiently greater than that by the amount necessary to give rise to the observed acceleration.

And so, if you plot these two quantities against each other — so, here's, kind of, 0, 0. Actually, this can be negative, but let's not go there.

1, 1. What you find out is that there's a kind of allowed region that sort of looks like this, allowed by the supernova data. Notice, this is — I'm assuming throughout that the dark energy really is the Cosmological Constant. I'm not thinking about Big Rip scenarios at the moment, because that would add a third dimension to this plot, and I don't want to do that just yet. So, this is all assuming that dark energy is the Cosmological Constant. But that's certainly a place to start. There's no reason not to do that.

And so, I've been kind of consistently claiming, as we've been talking about the course, that the real answer is somewhere like here. Yeah? That it's about .3 on the matter side, .25 and about 3/4, 2/3, 3/4 on the dark energy side. But, in fact, you could go — as far as the supernova care, you could have no matter at all and just a little dark energy, or you could have a lot of matter and a huge amount of dark energy. And you'd get the amount of acceleration, and therefore, satisfy the observational constraints.

But, in fact, it turns out, we know more than this, because there are other constraints on cosmology besides the supernovae. And, I have to tell you at this point that this course, the way I've presented it, is a little bit lopsided, because the other ways of constraining these two quantities are just as important as the supernovae, and I'm going to do them all in one lecture. And this is kind of in the spirit of the philosophy of this course, where we try and understand a few things in depth, rather than many things in breadth. But I'm going to talk about two other kinds of constraints on cosmology today, which are, in fact, just as important to modern cosmology as the supernovae are.

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