Primordial reheating in $f(R)$ cosmology by spontaneous decay of scalarons

TL;DR

This paper investigates the reheating process after inflation in $f(R)$ gravity models, focusing on particle creation constrained by quantum mechanics, and estimates reheating temperatures based on scalaron decay.

Contribution

It introduces a quantum mechanically consistent scenario for primordial reheating in $f(R)$ gravity, linking particle creation to scalaron decay and estimating reheating temperatures from a single parameter.

Findings

Reheating occurs over $ ext{~}10^{11}$ Planck times with a preheating stage of $ ext{~}10^{5}$ Planck times.

Reheating temperature estimated at $10^{13}$ GeV, with initial thermilization at $10^{12}$ GeV.

Energy density growth is negligible during inflation but significant during reheating.

Abstract

We employ a viable $f(R)$ gravity model capable of giving an inflationary phase in order to study the subsequent reheating phase due to particle creation at the expense of energy in the scalaron field. Since quantum mechanics is expected to play a dominant role in particle creation, we formulate a plausible scenario of reheating obeying Heisenberg's uncertainty principle that imposes constraints on the particles created in the configuration space. We show that, so long as the energy available in the scalaron field is sufficient to populate the entire configuration space, the energy density of the particles grows, attaining a maximum value giving an efficient reheating. Beyond this maximum, the available energy becomes insufficient to populate the entire configuration space leading to a declining energy density. We further find that there is a negligible growth of energy density in the inflationary phase that lasts for $\sim 10^7 \, t_{\rm P}$, although particles are constantly created in this phase. The subsequent reheating phase spans for $\sim10^{11} \, t_{\rm P}$ and it begins with a well-defined preheating stage lasting for $\sim 10^{5} \, t_{\rm P}$, making a cross-over to a thermilization regime. The temperature at the beginning of the thermilization is found to be $T_{\rm th}\sim 10^{12}$ GeV, whereas the reheating temperature is estimated as $T_{r}\sim10^{13}$ GeV. Importantly, these estimates follow from a single parameter, the scalaron mass, $M\sim10^{-5} \, M_{\rm P}$.