Tachyonic gravitational dark matter production after inflation

TL;DR

This paper introduces a new gravitational mechanism for non-thermal dark matter production after inflation, utilizing curvature-induced tachyonic instabilities in a scalar field coupled to spacetime curvature invariants.

Contribution

It presents a novel framework where curvature-driven tachyonic instabilities produce dark matter, validated through analytical estimates and lattice simulations, applicable across various masses and inflationary scales.

Findings

The mechanism can reproduce the observed dark matter relic density.

Tachyonic instabilities are triggered by rapid curvature changes at inflation's end.

A fitting function allows lattice-independent application of results.

Abstract

We propose a novel gravitational mechanism for the non-thermal production of dark matter driven by curvature-induced tachyonic instabilities after inflation. Departing from the commonly studied non-minimal couplings to gravity, our framework considers a real spectator scalar field coupled quadratically to spacetime curvature invariants. We show that the rapid reorganization of spacetime curvature at the end of inflation can dynamically render the dark matter field tachyonic, triggering a short-lived phase of spontaneous symmetry breaking and explosive particle production. As a concrete and theoretically controlled example, we focus on the Gauss-Bonnet topological invariant. By combining analytical estimates with $3+1$ classical lattice simulations in the spectator field approximation, we track the out-of-equilibrium evolution of the system and compute the resulting dark matter abundance. We find that this purely gravitational mechanism can robustly reproduce the observed dark matter relic density over a wide range of masses and inflationary scales, providing also a simple fitting function that enables a lattice-independent application of our results.