Reheating constraints to inflationary models

TL;DR

This paper explores how reheating phase constraints can refine inflationary models, linking the spectral index to reheating temperature, and suggests future measurements can distinguish between different inflation scenarios.

Contribution

It introduces a method to constrain inflationary models using reheating parameters and spectral index measurements, providing new links between reheating temperature and observable spectral features.

Findings

Canonical reheating is consistent with $eta=0$ for $ _s$ within current bounds.

Reheating temperature $T_{re}$ is related to $n_s$; higher $T_{re}$ implies $n_s$ near 0.965.

Different inflation models impose specific constraints on the reheating equation-of-state parameter.

Abstract

Evidence from the BICEP2 experiment for a significant gravitational-wave background has focussed attention on inflaton potentials $V(\phi) \propto \phi^\alpha$ with $\alpha=2$ ("chaotic" or "$m^2\phi^2$" inflation) or with smaller values of $\alpha$, as may arise in axion-monodromy models. Here we show that reheating considerations may provide additional constraints to these models. The reheating phase preceding the radiation era is modeled by an effective equation-of-state parameter $w_{\rm re}$. The canonical reheating scenario is then described by $w_{\rm re}=0$. The simplest $\alpha=2$ models are consistent with $w_{\rm re} = 0$ for values of $n_s$ well within the current $1\sigma$ range. Models with $\alpha=1$ or $\alpha=2/3$ require a more exotic reheating phase, with $-1/3<w_{\rm re}<0$, unless $n_s$ falls above the current $1\sigma$ range. Likewise, models with $\alpha=4$ require a physically implausible $w_{\rm re}>1/3$, unless $n_s$ is close to the lower limit of the $2\sigma$ range. For $m^2\phi^2$ inflation and canonical reheating as a benchmark, we derive a relation $\log_{10}\left(T_{\rm re}/10^6\,{\rm GeV} \right) \simeq 2000\,(n_s-0.96)$ between the reheat temperature $T_{\rm re}$ and the scalar spectral index $n_s$. Thus, if $n_s$ is close to its central value, then $T_{\rm re}\lesssim 10^6$~GeV, just above the electroweak scale. If the reheat temperature is higher, as many theorists may prefer, then the scalar spectral index should be closer to $n_s\simeq0.965$ (at the pivot scale $k=0.05\,{\rm Mpc}^{-1}$), near the upper limit of the $1\sigma$ error range. Improved precision in the measurement of $n_s$ should allow $m^2\phi^2$, axion-monodromy, and $\phi^4$ models to be distinguished, even without precise measurement of $r$, and to test the $m^2\phi^2$ expectation of $n_s\simeq0.965$.