Scalar Field Fluctuations and the Production of Dark Matter

Garcia, Marcos A.G.; Ke, Wenqi; Mambrini, Yann; Olive, Keith A.; Verner, Sarunas

Scalar Field Fluctuations and the Production of Dark Matter

Feb 27, 2025

57 pages

e-Print:

2502.20471 [hep-ph]

Report number:

UMN--TH--4417/25,
FTPI--MINN--25/02

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Abstract: (arXiv)

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.

Note:

57 pages, 11 figures

References(121)

Figures(14)

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