[Paper Review] Dark matter production via a non-minimal coupling to gravity

Oleg Lebedev, Timofey Solomko+1 more|arXiv (Cornell University)|Nov 21, 2022

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper investigates non-thermal dark matter production via a non-minimal coupling to gravity ($\xi R s^2$) during inflaton oscillations. Using lattice simulations, it shows that for $\xi \gtrsim 5$, resonant production occurs, while backreaction and rescattering suppress efficiency at $\xi > 30$, leading to quasi-equilibrium and a $\xi$-independent dark matter yield at $\xi \gtrsim 100$, with the correct relic abundance achievable across a broad mass range.

ABSTRACT

We study postinflationary scalar dark matter production via its non-minimal coupling to gravity. During the inflaton oscillation epoch, dark matter is produced resonantly for a sufficiently large non-minimal coupling $ξ\gtrsim 5$. We find that backreaction on the curvature and rescattering effects typically become important for the values of $ξ$ above $30$, which invalidate simple estimates of the production efficiency. At large couplings, the dark matter yield becomes almost independent of $ξ$, signifying approximate quasi-equilibrium in the inflaton-dark matter system. Although the analysis gets complicated by the presence of apparent negative energy in the Jordan frame, this behaviour can be regularized by introducing mild dark matter self-interaction. Using lattice simulations, we delineate parameter space leading to the correct dark matter relic abundance.

Motivation & Objective

• To investigate dark matter production via non-minimal coupling to gravity in the post-inflationary era.
• To assess the impact of collective effects—backreaction and rescattering—on dark matter abundance at large coupling strengths.
• To determine parameter space yielding the correct observed dark matter relic density using lattice simulations.
• To resolve apparent negative energy in the Jordan frame through mild self-interaction and particle number conservation.
• To compare outcomes for quadratic and quartic inflaton potentials in the context of non-thermal dark matter production.

Proposed method

• Lattice simulations are employed to model the inflaton-DM system in the Jordan frame, avoiding instabilities from field-dependent kinetic terms in the Einstein frame.
• The action includes a non-minimal coupling $\mathcal{L}_{\xi} = -\frac{1}{2}\xi R s^2$, leading to time-varying effective mass for $s$ during inflaton oscillations.
• The simulation tracks energy density, particle number, and occupation numbers, with initial conditions set to the vacuum state for $s$.
• A small self-coupling $\lambda_s$ is introduced to regularize negative energy densities arising from scalar-graviton mixing in the Jordan frame.
• The analysis is performed for both quadratic and quartic inflaton potentials, with $m_\phi \gg m_s$ to suppress inflationary fluctuations.
• Observables are extracted at $a/a_0 \sim 10^3$, where the system approaches late-time behavior and particle number is conserved.

Experimental results

Research questions

• RQ1 How does non-minimal coupling to gravity ($\xi R s^2$) lead to resonant dark matter production during inflaton oscillations?
• RQ2 What is the role of backreaction and rescattering in modifying dark matter production efficiency at large $\xi$?
• RQ3 Can negative energy densities in the Jordan frame be regularized to yield a physically meaningful particle number?
• RQ4 At what value of $\xi$ does the system approach quasi-equilibrium, and how does this affect the final dark matter abundance?
• RQ5 What parameter ranges of $\xi$, $m_s$, and $\lambda_s$ yield the correct observed dark matter relic density?

Key findings

• Resonant dark matter production occurs for $\xi \gtrsim 5$ due to tachyonic growth from oscillating curvature.
• For $\xi > 30$, backreaction and rescattering significantly suppress production efficiency, invalidating simple estimates.
• At $\xi \gtrsim 100$, the system approaches quasi-equilibrium, leading to a dark matter yield nearly independent of $\xi$.
• The inclusion of a small self-coupling $\lambda_s \sim 10^{-6}$ regularizes negative energy densities and ensures conserved particle number in the Jordan frame.
• For $\xi = 100$, dark matter can constitute up to 20% of the total energy density at the end of resonance, scaling as radiation.
• The mechanism produces the correct relic abundance across a wide range of dark matter masses, particularly for $\xi \gtrsim 100$.