Thermalization after/during Reheating

If reheating of the Universe takes place via Planck-suppressed decay, it seems that the thermalization of produced particles might be delayed, since they have large energy/small number densities and number violating large angle scatterings which decrease the momentum of particles by large amount are inefficient correspondingly. In this paper, we study the thermalization of such "under occupied" decay products in detail, following recent developments in understanding the thermalization of non-abelian plasma. Contrary to the above naive expectation, it is shown that in most cases thermalization after/during reheating occurs instantaneously by properly taking account of scatterings with small angles and of particles with small momenta. In particular, the condition for instantaneous thermalization before the completion of reheating is found to be $\alpha^{8/5} \gg (m_\phi / M_{\rm pl}) (M_{\rm pl}^2 \Gamma_\phi / m_\phi^3)^{1/5}$, which is much milder than that obtained in previous works with small angle scatterings taken into account.