Scalar Field Fluctuations and the Production of Dark Matter

TL;DR

This paper analyzes how scalar field fluctuations during inflation can produce dark matter, exploring various interaction scenarios and their impact on relic abundance and observational constraints.

Contribution

It provides a comprehensive analysis of scalar field evolution during inflation, including self-interactions and inflaton couplings, expanding the viable parameter space for dark matter candidates.

Findings

Non-interacting scalar requires very high mass and low reheating temperature.

Self-interactions and inflaton couplings allow for lighter scalar dark matter.

Constraints from isocurvature fluctuations and condensate fragmentation are considered.

Abstract

One of the simplest possible candidates for dark matter is a stable scalar singlet beyond the Standard Model. If its mass is below the Hubble scale during inflation, long-wavelength modes of this scalar will be excited during inflation, and their subsequent evolution may lead to the correct relic density of dark matter. In this work, we provide a comprehensive analysis of the evolution of a spectator scalar. We examine three cases: (1) a non-interacting massive scalar, (2) a massive scalar with self-interactions of the form $\lambda_\chi \chi^p$, and (3) a massive scalar coupled to the inflaton $\phi$ through an interaction term of the form $\sigma_{n,m} \phi^n \chi^m$. In all cases, we assume minimal coupling to gravity and compare these results with the production of short-wavelength modes arising from single graviton exchange. The evolution is tracked during the reheating phase. Our findings are summarized using $(m_\chi, T_{\rm RH})$ parameter planes, where $m_\chi$ is the mass of the scalar field and $T_{\rm RH}$ is the reheating temperature after inflation. The non-interacting scalar is highly constrained, requiring $m_\chi > 3 \times 10^{12}~\rm {GeV}$ and $ T_{\rm RH} \lesssim 7~\text{TeV}$ for an inflationary potential with a quadratic minimum. However, when self-interactions or couplings to the inflaton are included, the viable parameter space expands considerably. In these cases, sub-GeV and even sub-eV scalar masses can yield the correct relic abundance, opening new possibilities for light dark matter candidates. In all cases, we also impose additional constraints arising from the production of isocurvature fluctuations, the prevention of a secondary inflationary phase triggered by the spectator field, and the fragmentation of scalar condensates.