[논문 리뷰] Tachyonic gravitational dark matter production after inflation

Giorgio Laverda, Tomás Mendes외 1명|arXiv (Cornell University)|2026. 01. 12.

Cosmology and Gravitation Theories인용 수 0

한 줄 요약

논문은 팽창 후 곡률 유도 타코니ック 불안정성에 의한 비열적 다크 매터 생산을 순전히 중력적 메커니즘으로 제안하며, Gauss–Bonnet 불변량에 초점을 두고 분석적 추정과 3+1 격자 시뮬레이션으로 관측된 잔류 밀도와 일치함을 검증한다.

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 fully non-linear $3+1$ classical lattice simulations, 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.

연구 동기 및 목표

• Motivate and formulate a gravitational EFT framework where curvature induces a tachyonic instability for a spectator dark matter field.
• Identify curvature operators, especially Gauss–Bonnet, that trigger symmetry breaking across cosmological epochs.
• Develop analytical and numerical methods to track non-equilibrium evolution and compute the resulting DM abundance.
• Demonstrate that the mechanism can reproduce the observed DM relic density over broad parameter ranges.
• Highlight potential observational imprints, such as stochastic gravitational waves, from the curvature-driven phase transition.

제안 방법

• Construct the EFT with a spectator scalar chi coupled quadratically to curvature invariants, leading to an effective mass M_eff^2 = M^2 + xi R + curvature^2 terms over Lambda^2.
• Specialize to a FLRW background and express curvature invariants in terms of the Hubble rate and equation of state to study sign changes in M_eff^2.
• Focus on quadratic curvature operators, particularly the Gauss–Bonnet combination, which yields a positive M_eff^2 during inflation and negative during radiation domination.
• Derive the equation of motion for chi, including tachyonic regimes, and analyze homogeneous and non-homogeneous (fluctuation) dynamics.
• Employ 3+1 classical lattice simulations to capture non-linear out-of-equilibrium evolution and compute the resulting DM relic abundance.
• Provide analytical estimates and a lattice-independent fitting function to apply results across parameter space.

실험 결과

연구 질문

• RQ1 Can curvature-induced quadratic invariants trigger a transient tachyonic instability in a spectator dark sector after inflation?
• RQ2 Under Gauss–Bonnet-type couplings, does a sign change in the effective mass across the inflation–radiation transition robustly generate DM with the correct relic density?
• RQ3 What are the dominant contributions to dark matter production from tachyonic growth versus homogeneous condensate evolution?
• RQ4 How do the generated DM abundance and its evolution depend on the inflationary scale and the EFT cutoff?
• RQ5 What observable cosmological signatures (e.g., gravitational waves) can accompany this curvature-driven DM production?

주요 결과

• Curvature-induced tachyonic instabilities can drive explosive production of dark matter in a spectator sector after inflation.
• The Gauss–Bonnet invariant provides a robust mechanism: positive mass during inflation and negative mass during radiation domination, enabling a sign flip without fine-tuning.
• Numerical lattice simulations confirm efficient out-of-equilibrium production and allow computation of the resulting DM relic abundance across a wide parameter range.
• Analytical estimates, complemented by lattice results, yield a simple fitting function to apply results without lattice simulations.
• The mechanism can reproduce the observed DM density and links DM properties to the expansion history, potentially leaving imprints in cosmological observables such as stochastic gravitational waves.