Thermalisation after inflation
Sacha Davidson, Subir Sarkar
TL;DR
The paper investigates how inflaton decay products thermalise after inflation, focusing on whether energy loss and particle production occur rapidly enough to establish a thermal bath at the reheating temperature $T_{\rm reh}$. It shows that elastic $2\to2$ scattering, while infrared-enhanced, transfers energy slowly, whereas inelastic $2\to3$ processes efficiently generate gauge bosons and absorb energy, yielding a thermalisation rate $\Gamma_{\rm inel} \sim \alpha^3 T_{\rm reh}^2 / m_{\phi}$ and a thermalisation timescale $\tau_{\rm therm} \sim (\alpha^3 n_{\phi}/T_{\rm reh}^2)^{-1}$. The analysis indicates that reheating to $T_{\rm reh}$ via $2\to3$ interactions is feasible for plausible parameter ranges (e.g., $m_{\phi} \lesssim \alpha^3 M_{\rm Pl}$), and that soft inelastic processes play a crucial role in achieving kinetic and chemical equilibrium. Overall, the work highlights the primacy of inelastic scattering in setting the early-universe thermal history and has implications for baryogenesis and relic abundances tied to reheating.
Abstract
During (re)heating of the universe after inflation, the relativistic decay products of the inflaton field $φ$ 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 $α$, 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, $\sim(α^3 n_φ/T_{\reh}^2)^{-1}$.