Thermalisation after inflation

During (re)heating of the universe after inflation, the relativistic decay products of the inflaton field $\phi$ must lose energy and additional particles must be produced to attain a thermalised state at a temperature $T_{\reh}$. We estimate the rate of energy loss via elastic and inelastic scattering interactions. Elastic scattering is an inefficient energy loss mechanism so inelastic processes, although higher order in the coupling $\alpha$, can be faster because more energy is transfered. The timescale to produce a particle number density of ${\cal O}(T_{\reh}^3)$ is the inelastic energy loss timescale, $\sim(\alpha^3 n_\phi/T_{\reh}^2)^{-1}$.