## Wednesday, November 20, 2013

can you express the density parameter $\Omega_\gamma$ of a Planck-distributed relativistic species as a function of temperature only?
1. in fact, the energy density $\rho$ of a Planck-distributed quantum gas is just $\sigma T^4$ where $\sigma=\pi k_B^4/(15(\hbar c)^3)$ is the Stefan-Boltzmann constant and $T$ is the temperature. this can be expressed in units of the critical density $\rho_\mathrm{crit}=3H_0^2/(8\pi G)$: