# Homework Help: Cosmology problem

1. Mar 8, 2013

1. The problem statement, all variables and given/known data
i i am trying to derive $\dot{\rho_{R}}+4H\rho_{R}-\Gamma_{\phi}\rho_{\phi}=0$ as in Kolb an turner (Boltzmann describing reheating).

Is the correct approach to, use the 1st law dU=dQ-pdV, but what would dQ be?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 10, 2013

### clamtrox

That is just the equation of conservation of energy, with an extra term with transfers energy from the inflaton to radiation.

3. Mar 10, 2013

how though can it be derived?
I no that: $dU=(a^{3}\rho_{R})$ and $1/3\rho dV= pdV$, but Im not sure about dQ.

It is obviously then $\rho_R d(a^3)+a^{3}d\rho_{R}=dQ - 1/3\rho_{R}d(a^3)$ Then by dividing through by dt one can get $\dot{\rho}_{R}+4H\rho_{R} -\frac{dQ}{dt} =0$.

I don't see how one can justify $\Gamma_{\phi}\rho_{\phi}=\frac{dQ}{dt}$

4. Mar 10, 2013

### clamtrox

I don't see how you can justify using the first law in that form, when clearly in reheating the number of particles is not conserved. It's my understanding that the $\Gamma \rho$-term is just phenomenological.