Notes on Relativity and Cosmology - Physics Department, UCSB

306 CHAPTER 10. COSMOLOGY
these experiments will either confirm or deny the predictions of inflation in more
detail.
By the way, it is a rather strange picture of the universe with which we are left.
There are several confusing issues. One of them is “where does this vacuum
energy come from?” It turns out that there are some reasonable ideas on this
subject coming from quantum field theory... However, while they are all reasonable
ideas for creating a vacuum energy, they all predict a value that is 10 120
times too large. I will take a moment to state the obvious: 10 120 is an incredibly
huge number. A billion is ten to the ninth power, so 10 120 is one billion raised
to the thirteenth power. As a result, physicists are always asking, “Why is the
cosmological constant so small?”
Another issue is that, as we mentioned, Ω Λ and Ω matter do not stay constant in
time. They change, and in fact they change in different ways. There is a nice
diagram (also from Sean Carroll) showing how they change with time. I’ll hand
this out too. What you can see is that, more or less independently of where you
start, the universe naturally evolves toward Ω Λ = 1. On the other hand, back at
the big bang Ω Λ was almost certainly near zero. So, an interesting question is:
“why is Ω Λ only now in the middle ground (Ω Λ = .6), making it’s move between
zero and one?” For example, does this argue that the cosmological constant is
not really constant, and that there is some new physical principle that keeps
it in this middle ground? Otherwise, why should the value of the cosmological
constant be such that Ω Λ is just now making it’s debut? It is not clear why Λ
should not have a value such that it would have taken over long ago, or such
that it would still be way too tiny to notice.
10.5 The Beginning and The End
Well, we are nearly finished with our story but we are not yet at the end. We
traced the universe back to a time when it was so hot and dense that the nuclei
of atoms were just forming. We have seen that there is experimental evidence
(in the abundances of Hydrogen and Helium) that the universe actually was
this hot and dense in its distant past. Well, if our understanding of physics is
right, it must have been even hotter and more dense before. So, what was this
like? How hot and dense was it? From the perspective of general relativity,
the most natural idea is that the farther back we go, the hotter and denser it
was. Looking back in time, we expect that there was a time when it was so hot
that protons and neutrons themselves fell apart, and that the universe was full
of things called quarks. Farther back still, the universe so hot that our current
knowledge of physics is not sufficient to describe it. All kinds of weird things
might have happened, like maybe the universe had more than four dimensions
back then. Maybe the universe was filled with truly exotic particles. Maybe the
universe underwent various periods of inflation followed by relative quiet.
Anyway, looking very far back we expect that one would find conditions very
similar to those near the singularity of a black hole. This is called the ‘big bang