By what equation do physicists use to measure the time before the CMB

[robertjford80]

I'm reasonably convinced that physicists know what happened in the universe at certain temperatures: just find out what happens when you reach those temperatures in a particle accelerator. I still have yet to come across the equation that measures the time before the CMB and what the universe's temperature was at that time. Most physicists agree that the CMB occurred 379,000 years AB (after the BB). I'm assuming they know this because of an equation. Well, what is it?

 

[marcus]

the Friedmann equation gives the scale factor a(t) as a function of time. Temp depends on a(t).

The dependence is pretty simple back when most of the energy was in the form of radiation---a very hot bath of photons---the temp T(t) just goes as 1/a(t).

So all you have to do is solve the Friedmann equation which is an ordinary differential equation governing the scalefactor a(t).

It is a simplified version derived from the Einstein GR equation for the special case where stuff is uniformly distributed throughout space. Basically all you have is a density rho(t) and the scalefactor a(t) itself.
You normalize a(t) so that = 1 at present. And then you run the model back in time.

 

[robertjford80]

cool, thanks