Why is Omega_{Total} ~ 1? Why not 106? Why not 42? Why not 0.0021034011031?The density of the Universe changes with time, as the Universe expands. So Omega_{M}, the ratio of the actual density to the critical density also changes:
(Strictly speaking, this holds only for a matter dominated universe. But it's only recently that dark energy has started affecting the expansion of the universe, so early on the universe behaved like a matter dominated universe....)
Let's look at two examples.
- At a redshift of z=10,000 (ie when the universe was 10^{4} times smaller than now), it had a density parameter of 1.0001
- At a redshift of z=10,000, it had a density parameter of 0.9
In the universe that is slightly overdense at z=10^{4}, the density parameter today (at z=0) would be 100. In the universe that is slightly underdense at early times, we ought to measure a density parameter today of 0.001. Omega very quickly diverges from 1, unless it is equal to 1.
It gets worse. Look at this figure (from Ned Wright's Cosmology Tutorial): if the density of the universe had been ever so slightly non-critical 1 nanosecond after the big bang, we would have a drastically different universe:
Looking at the microwave background, it is very smooth to 1 part in 10^{5}. Everywhere. But at the time of recombination, regions of the universe which are now separated by more than 2 degrees on the sky were never in causal contact.
Think about the horizon distance:
At the time of the CMB, the horizon scale was about 0.25 Mpc. The current horizon distance is ~ 14.6 Gpc, so the observable universe at a redshift of z=1100 was 14.6 Gpc/1100 ~ 13.2 Mpc in size.
Therefore the angular size of a causally connected region at z=1100 is 0.25 Mpc / 13.2 Mpc = 0.02 radians ~ 1 degree.
So how did regions spanning the entire observable universe "know" that they should all be at exactly the same temperature?
But what drives inflation?
We don't know.