# Critical density in Early Times

1. Aug 21, 2010

### BillSaltLake

What was the total mass energy density at the time of recombination? Has it has it been measured by WMAP? (Edit: I think it's 4.28x10-18kg/m3 from the # of photons/volume in a 2979K blackbody, x baryon:photon ratio x proton mass x (1+ dark:baryon ratio) divided by the 0.755 matter fraction at the time.)

Assuming a flat Universe, in times before dark energy was significant, I think the critical density as a function of time was 3H2/(8 pi G), where
1) H = 1/(2t) during energy-domination (very early times), and
2) H = 2/(3t) during matter-domination.
Thus during matter-domination, the critical density was 1/(6 pi Gt2), and it was 9/16 of that during energy -domination.

I might expect the total energy density (matter + energy) at the time of recombination to be between the matter-dominated and energy-dominated numbers. (Edit: the WMAP appears to be between those numbers. Matter-dominated would be 5.43x10-18kg/m3) However, when I use a differential eq to solve it directly, I'm only getting 0.291 of the matter-dominated value of 1/(6 pi Gt2) where t is the recombination time. (Edit: I don't do math good. Sorry.)

Last edited: Aug 21, 2010
2. Aug 21, 2010

### cepheid

Staff Emeritus
I didn't look too closely at your work, but here's how I would approach this:

WMAP has measured Ωm. This matter density parameter is defined as follows:

Ωm ρm(t0) / ρcrit

where t0 means now and

ρcrit ≡ 3H02 / 8πG

We also know that

ρm(t) = ρm(t0)a-3. ​

So now we just need to know the scale factor of the universe at the time of recombination.

Last edited: Aug 21, 2010
3. Aug 22, 2010

1/1090