Light scalars on cosmological backgrounds

TL;DR

This paper investigates how a light, self-interacting scalar field behaves on various cosmological backgrounds, revealing that space curvature can significantly excite the field and impact phenomena like reheating and dark matter.

Contribution

It provides a general formula for the scalar field variance on curved backgrounds and explores new cases such as matter domination and kination.

Findings

Curvature induces significant scalar field excitation.

Self-regulation of infrared divergences occurs outside de Sitter space.

Effective mass from self-interaction affects cosmological processes.

Abstract

We study the behaviour of a light quartically self-interacting scalar field $\phi$ on curved backgrounds that may be described with the cosmological equation state parameter $w$. At leading order in the non-perturbative 2PI expansion we find a general formula for the variance $\langle\hat{\phi}^2\rangle$ and show for several previously unexplored cases, including matter domination and kination, that the curvature of space can induce a significant excitation of the field. We discuss how the generation of a non-zero variance for $w\neq-1$ can be understood as a process of self-regulation of the infrared divergences very similarly to what is known to occur in de Sitter space. To conclude, the appearance of an effective mass due to self-interaction is generic for a light scalar in curved space and can have important implications for reheating, vacuum stability and dark matter generation.