Cosmological Moduli Problem from Thermal Effects

TL;DR

This paper analyzes how thermal effects induce a minimal abundance of cosmological moduli, such as saxions, setting bounds on reheating temperatures and highlighting the inevitability of their presence due to thermal dynamics.

Contribution

It provides the first estimate of the minimal modulus abundance caused by thermal effects, applicable to a broad class of moduli including saxions, with implications for early universe cosmology.

Findings

Thermal effects necessarily induce a baseline modulus abundance.

The minimal modulus abundance constrains reheating temperatures.

Fine-tuning initial conditions cannot eliminate the thermal-induced modulus.

Abstract

We estimate the cosmological abundance of a modulus field that has dilatonic couplings to gauge fields, paying particular attention to thermal corrections on the modulus potential. We find that a certain amount of the modulus coherent oscillations is necessarily induced by a linear thermal effect. We argue that such an estimate provides the smallest possible modulus abundance for a given thermal history of the Universe. As an example we apply our results to a saxion, a bosonic supersymmetric partner of an axion, and derive a tight bound on the reheating temperature. We emphasize that the problem cannot be avoided by fine-tuning the initial deviation of the modulus field, since the minimal amount of the modulus is induced by the dynamics of the scalar potential.