# Motivating Inflation

Two observations, in particular, are extremely puzzling under the Big Bang model.

## The flatness problem

Why is OmegaTotal ~ 1? Why not 106? Why not 42? Why not 0.0021034011031?

The density of the Universe changes with time, as the Universe expands. So OmegaM, 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 universe that is slightly overdense at z=104, 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:

## 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?

Why is the universe flat? Why is the universe smooth?

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 standard 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. One possibility is that at this point the vacuum energy universe underwent a phase transition, at which point the strong nuclear force differentiated from the electroweak force. This phase transition may have released the energy which drove inflation.