Decoupling condition for dark matter WIMP

[shahbaznihal]

Hi,

I am a research student in Theoretical Dark Matter Cosmology. I am currently working on the evolution of dark matter WIMP in the early universe. I am trying to understand how to derive the famous condition for dark matter decoupling,T = m/26. How do you get this condition from the Boltzmann equation?

Any discussion or comments will be much appreciated. Thanks!

 

[Haelfix]

Hello,

The calculation you seek is a standard one in most textbooks on the subject, but unfortunately it is a numerical one, so its a little bit hard to just write it down for you in such a forum.

See the Tasi lectures on dark matter from 2008,
http://arxiv.org/abs/0901.4090
figure 1 is the curve you are looking for.

 

[shahbaznihal]

Okay, so it is a numerical solution. I had a feeling but was thinking if one can get it analytically someway. Thanks a lot for the reference though. Cheers!1