Inflaton decay in No-Scale Supergravity and Starobinsky-like models

TL;DR

This paper investigates the decay mechanisms of the inflaton in Starobinsky-like models derived from $R+R^2$ gravity and no-scale supergravity, analyzing how different couplings affect reheating temperatures and decay channels.

Contribution

It elucidates the inflaton decay processes in Starobinsky-like models, highlighting the effects of conformal coupling and anomaly-induced decays on reheating in both gravity and supergravity frameworks.

Findings

Reheating temperature is about 3 x 10^9 GeV with standard matter coupling.

Conformal coupling of the Higgs can suppress decay, but anomaly effects restore reheating to ~10^8 GeV.

Starobinsky potential in no-scale supergravity allows inflaton decay via superpotential or gauge kinetic function.

Abstract

We consider the decay of the inflaton in Starobinsky-like models arising from either an $R+R^2$ theory of gravity or $N=1$ no-scale supergravity models. If Standard Model matter is simply introduced to the $R + R^2$ theory, the inflaton (which appears when the theory is conformally transformed to the Einstein frame) couples to matter predominantly in Standard Model Higgs kinetic terms. This will typically lead to a reheating temperature of $\sim 3 \times 10^9$~GeV. However, if the Standard Model Higgs is conformally coupled to curvature, the decay rate may be suppressed and vanishes for a conformal coupling $\xi = 1/6$. Nevertheless, inflaton decays through the conformal anomaly leading to a reheating temperature of order $10^8$~GeV. The Starobinsky potential may also arise in no-scale supergravity. In this case, the inflaton decays if there is a direct coupling of the inflaton to matter in the superpotential or to gauge fields through the gauge kinetic function. We also discuss the relation between the theories and demonstrate the correspondence between the no-scale models and the conformally coupled $R+R^2$ theory (with $\xi = 1/6$).