Wednesday, October 9, 2013

equation of state of baryons

can you estimate the equation of state parameter $w$ for the baryonic component in the Universe?

bonus question: how would $w$ change in time?


  1. the tiny contribution to the rest mass due to kinetic energy in a baryon moving thermally with $T\simeq 3$K can be estimated to be:
    w =
    \simeq \frac{k_BT}{mc^2}
    if there's thermal equilibration, $k_BT\simeq \epsilon_\mathrm{kin}$. substituting numbers gives $w\simeq10^{-12}$, and this scales roughly with $T$.

  2. the time evolution depends on cosmology: assuming that the baryons evolve thermally for themselves, $T\propto 1/a$. the Friedmann-equation gives $\dot{a}/a=H_0$ in the dark energy dominated phase, which is solved for $a(t) \propto \exp(H_0 t)$, such that $T\propto \exp(-t)$.