Motivating Inflation

---

The flatness problem

Why is Omega₀ ~ 0.1 -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, 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 10⁴ 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 slightly overdense universe, we now ought to measure a density parameter of 1000. In the slightly underdense universe, we ought to measure a density parameter 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:

The Smoothness Problem

Looking at the microwave background, it is very smooth to 1 part in 10⁵. 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. How did all these regions of space "know" that they should all be at exactly the same temperature?

1980: Alan Guth dreams up inflation.

Let's say in the very early history of the universe it went through a phase of exponential expansion:  in 10^-24 seconds it expanded by a factor of 10⁵⁰. How would this fix the flatness and smoothness problems?
 
• flatness: imagining blowing up space by a factor of 10⁵⁰. Any curvature it had would be instantly "flattened".
• smoothness: originally the universe was smaller than the extrapolation of the expansion history to early epochs. So before inflation, everything was causally connected, then inflation drove things apart.


But what drives inflation?

We don't know.

Inflation is thought to have occurred when the Universe was only ~ 10^-34 seconds old, when the temperature was ~ 10²⁷ K. At this point the universe underwent a phase transition, as the strong nuclear force differentiated from the electroweak force. This phase transition may have released the energy which drove inflation.