1. Feb 9, 2017

### PeteSampras

When begin the radiation epoch with scale factor ~t1/2 ?

I read in some text that this begin at Planck time, but in other texs says that begin approx at 3 minutes.

2. Feb 9, 2017

### Buzz Bloom

Hi Pete:
I am not sure how to define the beginning and end of the radiation epoch, but I will take a crack at it.

The beginning
The radiation epoch must come after the inflation epoch ends, since the scale factor during inflation is
a ≈ et.​

Here is a quote from Wikipedia:
The inflationary epoch lasted from 10−36 seconds after the conjectured Big Bang singularity to sometime between 10−33 and 10−32 seconds after the singularity.
https://en.wikipedia.org/wiki/Inflation_(cosmology) .​

You are correct that the radiation epoch is characterized by
a ≈ t1/2.​

The end
I don't think there is a well defined criterion for this. The end will occur before ρr, the mass-energy density of radiation (photons) equals the mass-energy density of matter ρm. The problem is deciding on the value of the ratio
R = ρr : ρm > 1​
to use for the end of the radiation epoch and the start of the transition to the matter epoch. When that transition ends, the matter epoch is characterized by
a ≈ t2/3.​

If you specify the value you want to use for R, it is easy to calculate the value of a which corresponds to this R value. Calculating the corresponding value for t is more difficult.

Regards,
Buzz