Notes on Relativity and Cosmology - Physics Department, UCSB

302 CHAPTER 10. COSMOLOGY
Infinite Future
Deionization
Now
Big Bang Singularity
The regions we see at decoupling now have past light cones that overlap quite a
bit. So, they have access to much of the same information from the singularity.
In this picture, it is easier to understand how these entire universe could be at
close to the same temperature at decoupling.
Oh, to be consistent with what we know, this huge cosmological ‘constant’ has
to shut itself off long before decoupling. This is the hard part about making
inflation work. Making the cosmological constant turn off requires an amount of
fine tuning that many people feel is comparable to the one part in one-hundred
thousand level of inhomogeneities that inflation was designed to explain.
Luckily, inflation makes certain predictions about the detailed form of the cosmic
microwave background. The modern balloon experiments are beginning to probe
the interesting regime of accuracy, and it is hoped that MAP and PLANCK will
have some definitive commentary on whether inflation is or is not the correct
explanation.
10.4.4 Looking for mass in all the wrong places
Actually, there is a third chapter in our discussion of the cosmological constant.
You see, it turns out that the supernovae results and the CMB do not really
measure Λ directly, but instead link the cosmological constant to the overall
density of matter in the universe. So, to get a real handle on things, one has to
know the density of more or less regular matter in the universe as well.
Before we get into how much matter there actually is (and how we find out),
I need to tell you about the somewhat funny language that cosmologists use
to discuss this question. To get the idea, I’ll need to bring back the Einstein
equation, and this time I’ll add in a part to describe the cosmological constant.
As a change from before though, I’ll write it in terms of the Hubble expansion
rate H = 1 da
a dt .
H 2 − 8πGρ
3
− Λ 3 + ka−2 c 2 = 0. (10.6)
The cosmologists like to reorganize this equation by dividing by H 2 . This gives