# Exponential expansion of inflation

• I
The expansion of the inflationary universe is said to be roughly exponential. Why is it called "roughly" exponential?

PeterDonis
Mentor
The expansion of the inflationary universe is said to be roughly exponential.

In what source? Please give a specific reference.

It's mentioned in most cosmology texts, e.g. Cosmology by Steven Weinberg, in Inflation chapter.

PeterDonis
Mentor
It's mentioned in most cosmology texts, e.g. Cosmology by Steven Weinberg, in Inflation chapter.

Ok, so can you give a specific quote and page/section reference?

".....there was an earlier period of inflation, when the energy density of the universe was dominated by a slowly varying vacuum energy, and a(t) grew more or less exponentially." Pg. 201.

PeterDonis
Mentor
I would say the "more or less exponentially" is a consequence of the "slowly varying vacuum energy". As I understand it, only a vacuum energy that is exactly constant will lead to an expansion that is exactly exponential.

Chalnoth
I would say the "more or less exponentially" is a consequence of the "slowly varying vacuum energy". As I understand it, only a vacuum energy that is exactly constant will lead to an expansion that is exactly exponential.
It's more that only in a universe with nothing in it but vacuum energy will the expansion be exactly exponential. It's not quite exponential because there's other matter around.

PeterDonis
Mentor
It's not quite exponential because there's other matter around.

Is there, though? As I understand the basic inflation model, the Standard Model fields are all in their vacuum states during inflation, and all of these fields have zero vacuum expectation value for energy; they only get reheated to highly non-vacuum, high temperature states at the end of inflation.

Chalnoth