# Density Parameter for radiation dominated universe

1. ### ibysaiyan

442
Greetings everyone ,
Can anyone point me into the right direction on how to come out with a value/ expression for the density parameter of a radiation dominated universe.

Things that I know of/ can recall are:

Friedmann equation :
$$8/3 \pi G ρ R^2 -kc^2$$

Also when radiation dominates matter then we get ρ = 1/R^4 ( I think)

Density parameter :
So what am I missing to give me the density parameter ? $\Omega_{m}$ = $\rho / \rho_{critical}$
where
$\rho_{critical}= (3H^2 q / 4Pi G)$
Any sort of help is appreciated.

-ibysaiyan

Last edited by a moderator: Feb 22, 2012
2. ### cristo

8,411
Staff Emeritus
Your post doesn't make much sense. Your Friedmann 'equation' is not an equation, since you do not have an equals sign. You don't define R, or any of your other variables. But it's not really clear what you want to find -- an expression for $\Omega_R$ in terms of what?

3. ### ibysaiyan

442
I am sorry about that , the LHS should have (dR/dT)^2 for this to become the Friedmann equation anyways.. what I want is the density parameter of a radiation dominated universe.
I.e density at that state / critical density.

4. ### ibysaiyan

442
Oh i have figured it out that the deceleration parameter at the radiation dominated epoch is equivalent to the ratio of density at that time / critical density ( Omega) .