Thermalisation after inflation

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