An upper bound on the reheat temperature for short duration inflation

TL;DR

This paper derives a new upper limit on the reheating temperature after inflation based on gravitational wave non-observation, specifically for minimal-duration inflation scenarios, impacting primordial black hole research.

Contribution

It provides a novel upper bound on reheating temperature for short inflation durations, refining previous constraints based on gravitational wave data.

Findings

Reheating temperature bound: $T_{reh} \\lesssim 1.7 imes 10^{13}$ GeV.

Bound is significantly lower (by a factor of 428) than the standard gravitational wave-based limit.

Longer inflation durations relax the bound to the conventional limit.

Abstract

We calculate the upper bound on the reheating temperature given the non-observation of gravitational waves if the number of efolds during inflation are the minimum number required to address the horizon problem as formulated in terms of entropy. This bound is valid for canonical single field slow roll inflation with a generic potential. Our bound numerically is $T_{\text{reh}}\lesssim1.7\times10^{13}$ GeV, which is a factor of 428 less the usual bound one obtains from the non-observation of gravitational waves alone. If inflation lasted much longer than the minimum number of required efolds, our bound relaxes to coincide with the usual bound. We discuss the relevance for studies of primordial black holes.