Frontiers and Controversies in Astrophysics: Lecture 19 Transcript
April 10, 2007
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Professor Charles Bailyn:
Okay, we're talking about the origin and fate of the Universe. And let me remind
you of the story so far. There are basically two sets of observations that are important here. One is the
existence of the Hubble Diagram and Hubble's Law, which is the observational relationship between distance
and velocity for galaxies. And this leads you to the idea of a universal expansion. And the other is what we
discussed last time: that if you look back into the past, if you observe at a large distance--that is to say, a large
lookback time--what you discover is that things were different in the past. That the Universe, as a whole,
looked somewhat different and, in particular, was significantly denser, which is exactly what you would
predict if the Universe was expanding.
And these two things--these two observational facts put together are really what lead to the idea of a Universe
with a Big Bang cosmology. And this is great because you can then use this assumption that everything is
governed by the scale factor of the Universe. And the scale factor starts either at zero, or very close to zero,
and gets bigger with time.
And you can use that concept to do all sorts of wonderful things. You can describe the past. And in particular,
one of the things we did last time was to calculate the age of the Universe from the observations of the
Hubble Constant. And you can predict the future. And the future depends on how the expansion of the scale
factor changes. If the scale factor just continues to expand at its current rate, the Universe will continue to
expand and gradually get sparser and sparser, and colder and colder, and more and more boring.
But it's not expected that the expansion rate stays the same. It's expected that the expansion rate will change.
And, in particular, it's expected that the expansion rate will slow down. Why? Because there's matter in the
Universe, and matter exerts gravity, and gravity tends to pull things back together again.
And so, this is where we ended up last time. If you assume that gravity is the dominant force--that is to say
that any changes in the expansion rate of the Universe will be due to gravity, then, you can derive this critical
density, which we did last time, which is a quantity equal to 3
H
2
/ 8 Ï€
G
.
H
, you measure. The other things
are just constants, and you can calculate what this quantity is. Now, at this point, let me write down a piece of
astronomical jargon, which I didn't do last time.
The actual density of the Universe, divided by this critical density, is given a letter of its own. This is written
down as a capital Omega. So Î© is the true--the actual density of the Universe, whatever that turns out to be,
divided by the critical density. And then, you can describe the future of the Universe, depending on what Î©
is. If Î© is greater than 1, that means that the density's greater than the critical density. And this leads to
re-collapse and the "Big Crunch"--whereas, if Î© is less than 1, the Universe expands forever.