Dark matter production via a non-minimal coupling to gravity

TL;DR

This work analyzes postinflationary production of a real scalar dark matter field $s$ through its non-minimal coupling to gravity, $\xi R s^2$, using lattice simulations to capture backreaction and rescattering effects. The authors show that resonant production is efficient for $\xi \gtrsim 5$, with backreaction on curvature and mode-mode rescattering becoming important for $\xi \gtrsim 30$, and that at large $\xi$ the system approaches a quasi-equilibrium where the DM yield becomes nearly independent of $\xi$. A mild dark matter self-interaction $\lambda_s$ regularizes negative-energy issues in the Jordan frame, enabling a well-defined conserved particle number at late times. By mapping the parameter space and linking the preheating dynamics to reheating through a Higgs portal, the paper delineates regions that yield the correct DM relic abundance for both quartic and quadratic inflaton potentials, emphasizing the role of collective effects in shaping the final abundance and the potential UV-origin uncertainties from quantum gravity.

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.

Figures (7)

• Figure 1: Stability charts for the ellipsoidal wave equation \ref{['ch-4']}. Left:$\xi >0$; right:$\xi <0$. The color coding represents the Floquet exponent. The straight lines show an example of the time evolution of the coefficients for the zero and most excited $k_\textrm{max}$ modes at $\xi=30$.
• Figure 2: Curvature and DM variance evolution in the quartic inflaton potential at $\xi=50$ and $\lambda_s=0$. The resonance terminates at $a\sim 4$.
• Figure 3: The couplings producing the correct DM abundance in the quartic inflaton potential with the initial condition $\Phi_0 \simeq 0.9 \,M_\textrm{Pl}$. The area above the curve is ruled out by overabundance of dark matter. The reheating temperature can be read off from the $y$-axis on the right. The results for other DM masses are obtained by a simple rescaling according to \ref{['sigma-DM-eq-1']}.
• Figure 4: Relative contributions of the inflaton ($\rho_\phi$) and dark matter ($\rho_s$) to the total energy density in the Jordan frame. At early times, $\rho_s$ can be negative (dashed line) due to the scalar-graviton mixing. At late times, the particle number is conserved.
• Figure 5: Stability charts for the Mathieu equation. Left:$\xi>0$; right:$\xi<0$. The color coding represents the Floquet exponent.