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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 1/4 and 0.

1/4 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 1/4 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 1/4 of — the Ωmatter is 1/4, but there's a whole bunch of dark energy. 3/4 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.

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 1/4 and 0.

1/4 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 1/4 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 1/4 of — the Ωmatter is 1/4, but there's a whole bunch of dark energy. 3/4 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.

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