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## Main Question or Discussion Point

Hi everyone,

Can anyone point me into the right direction on how to compute the deceleration parameter (##q_0##) for a radiation dominated universe?

I know that q

So for a radiation dominated universe, we have ##\omega = + \frac{1}{3}##. And ρ~1/a

My notes say ##\Omega _{rad} = 8.2 \times 10^-5## but I'm not sure how this was calculated. How do I compute Ω

Using that value I get the following but I'm not sure if it's correct:

##q_0 = \frac{\Omega_0}{2} = \frac{8.2 \times 10^-5}{2} = 4.1 \times 10^{-5}##.

I couldn't find any info on this computation online. So any help is greatly appreciated.

Can anyone point me into the right direction on how to compute the deceleration parameter (##q_0##) for a radiation dominated universe?

I know that q

_{0}is given by##q_0=-\frac{\ddot{a}(t_0)}{a(t_0) H^2 (t_0)} = - \frac{\ddot{a}(t_0) a(t_0)}{\dot{a}^2(t_0)}=\frac{\Omega_0}{2}##

So for a radiation dominated universe, we have ##\omega = + \frac{1}{3}##. And ρ~1/a

^{4}, and a~t^{1/2}. I'm not sure how to relate this to that equation.My notes say ##\Omega _{rad} = 8.2 \times 10^-5## but I'm not sure how this was calculated. How do I compute Ω

_{0}=ρ/ρ_{crit}in this case? I know that ρ_{crit}=3H^{2}/8πG, but what is the density ρ?Using that value I get the following but I'm not sure if it's correct:

##q_0 = \frac{\Omega_0}{2} = \frac{8.2 \times 10^-5}{2} = 4.1 \times 10^{-5}##.

I couldn't find any info on this computation online. So any help is greatly appreciated.

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