Light scalars on cosmological backgrounds

Abstract

We study the behaviour of a light quartically self-interacting scalar field $\varphi$ 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 $⟨{\hat{\varphi }}^2⟩$ 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 $w\ne -1$ 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.

16 pages, 1 figure. v2: 18 pages with expanded discussion, improved structure and updated references. v3: several improvements and updated references, to be published in JHEP

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