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Gravitational dark matter production from fermionic spectator fields during inflation

Alessio Belfiglio, Orlando Luongo

TL;DR

This work analyzes gravitational particle production (GPP) of a minimally coupled fermionic spectator field during inflation as a mechanism to generate dark matter. It shows that inflaton-induced metric perturbations can drive a perturbative GPP channel that dominates over standard non-perturbative production when $m \ll H_I$, using the Weyl tensor formalism to compute the second-order contribution $N^{(2)}$. With Planck-consistent $H_I$ and two representative potentials—the Starobinsky and a quadratic hilltop model—the study finds that a Dirac spectator with mass in the range $10^5$–$10^7$ GeV can account for the observed DM abundance, $\Omega_{\rm DM} \simeq 0.12/h^2$. The results imply a blue-tilted geometric spectrum and indicate that reheating-era gravitational processes could further modify the total DM yield, motivating more detailed late-stage modeling and extensions to other particle spins and couplings.

Abstract

We investigate the gravitational particle production from vacuum for a minimally coupled fermionic spectator field during a single-field inflationary phase. We observe that metric perturbations arising from the quantum fluctuations of a scalar inflaton field enhance gravitational production, showing that such a perturbative contribution becomes dominant if the field mass is sufficiently smaller than the inflationary Hubble rate. We focus on modes that leave the Hubble horizon during the latest stages of slow-roll and we numerically compute the total number of particles obtained from perturbations, providing a lower bound on the amount of such \enquote{geometric} particles for the case of Starobinsky inflation and a quadratic hilltop scenario. Our outcomes are compatible with the net observational cold dark matter abundance as experimentally measured, whose dark matter candidate exhibits mass in the range $10^5 \lesssim m \lesssim 10^7$ GeV, excluded by previous non-perturbative calculations.

Gravitational dark matter production from fermionic spectator fields during inflation

TL;DR

This work analyzes gravitational particle production (GPP) of a minimally coupled fermionic spectator field during inflation as a mechanism to generate dark matter. It shows that inflaton-induced metric perturbations can drive a perturbative GPP channel that dominates over standard non-perturbative production when , using the Weyl tensor formalism to compute the second-order contribution . With Planck-consistent and two representative potentials—the Starobinsky and a quadratic hilltop model—the study finds that a Dirac spectator with mass in the range – GeV can account for the observed DM abundance, . The results imply a blue-tilted geometric spectrum and indicate that reheating-era gravitational processes could further modify the total DM yield, motivating more detailed late-stage modeling and extensions to other particle spins and couplings.

Abstract

We investigate the gravitational particle production from vacuum for a minimally coupled fermionic spectator field during a single-field inflationary phase. We observe that metric perturbations arising from the quantum fluctuations of a scalar inflaton field enhance gravitational production, showing that such a perturbative contribution becomes dominant if the field mass is sufficiently smaller than the inflationary Hubble rate. We focus on modes that leave the Hubble horizon during the latest stages of slow-roll and we numerically compute the total number of particles obtained from perturbations, providing a lower bound on the amount of such \enquote{geometric} particles for the case of Starobinsky inflation and a quadratic hilltop scenario. Our outcomes are compatible with the net observational cold dark matter abundance as experimentally measured, whose dark matter candidate exhibits mass in the range GeV, excluded by previous non-perturbative calculations.

Paper Structure

This paper contains 7 sections, 25 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Inflationary set up
  3. Incorporating a fermionic spectator field
  4. Perturbative GPP
  5. Geometric contribution to dark matter
  6. Including particle contribution during reheating
  7. Physical interpretation and final remarks

Figures (1)

  • Figure 1: Comoving number density $a^3 n^{(0)}$ as function of the Dirac field mass $m$, in a model which assumes instantaneous transition from inflation to the radiation era PhysRevD.101.123522. The required DM energy density, corresponding to the black dot, is computed as $m a^3 n^{(0)}$, in agreement with a cold DM component today. Within this model, non-perturbative GPP cannot account by itself for the current DM abundance if $m \leq 7.8 \times 10^8$ GeV, which corresponds to the shaded region.