Influence of spatial curvature in cosmological particle production

TL;DR

This paper investigates how different spatial curvatures in the early universe influence particle production during cosmic expansion, revealing significant effects especially for light fields and curved geometries.

Contribution

It provides analytical insights into curvature effects on cosmological particle production, including exact mode functions and non-perturbative particle number calculations for various curvature scenarios.

Findings

Spatial curvature markedly affects particle spectra, especially for light fields.

Deviations from flat-space results can reach several orders of magnitude.

Analytical models for both instantaneous and smooth inflation exit scenarios.

Abstract

We analyze cosmological particle production driven by spacetime expansion in the early universe for homogeneous and isotropic cosmologies with positive, negative, and zero spatial curvature. We prioritize analytical results to gain a deeper understanding of curvature-induced effects. Specifically, for a conformally coupled scalar field, we model the inflationary epoch as an exact de Sitter phase followed by a transition to a static universe. Both instantaneous and smooth exits from inflation are considered, the latter being implemented via the adiabatic vacuum prescription. Starting from an initial Bunch-Davies vacuum, we derive the associated mode functions carefully adapted to each curvature sign. Using the Bogoliubov formalism, we non-perturbatively compute the number density of produced scalar particles. Our results demonstrate that spatial curvature significantly impacts the resulting particle spectra, particularly for light fields, where the deviation from the flat-space scenario is most prominent and can reach several orders of magnitude