Tachyonic gravitational dark matter production after inflation

TL;DR

This work introduces a purely gravitational mechanism for dark matter production driven by curvature-induced tachyonic instabilities after inflation. By coupling a real spectator scalar χ to curvature invariants within a controlled gravitational EFT and focusing on the Gauss–Bonnet combination, the authors demonstrate that a rapid inflation-to-Radiation Dominated transition can flip the effective mass, trigger spontaneous symmetry breaking, and explosively generate χ excitations. Analytical insights complemented by fully non-linear 3+1 lattice simulations show that the resulting relic abundance can match the observed DM density across a wide parameter space, with a compact lattice-derived fitting formula enabling lattice-independent predictions. The scenario yields a non-thermal, IR-dominated DM population whose later evolution naturally transitions from radiation-like to matter-like behavior, and it opens avenues for signatures in gravitational waves and extensions to other dark-sector configurations.

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.

Figures (12)

• Figure 1: Allowed regions in the $(\gamma,\beta)$ parameter space for which the curvature-induced contribution to $M_{\rm eff}^2$ becomes negative, triggering a spontaneous symmetry breaking of the $\mathbb{Z}_2$ symmetry of the spectator field for sufficiently small bare masses $M$. The regions are shown for fixed $\alpha=1$, $\xi=4$ and $\Lambda=H_*$ and correspond to different post-inflationary cosmological epochs, classified by their average equation of state $w$ — MD (Matter Domination), RD (Radiation Domination) and KD (Kinetic Domination). The black dot corresponds to the benchmark Gauss-Bonnet scenario considered in this paper, $(\alpha,\beta,\gamma)=(1,-4,1)$.
• Figure 2: Time evolution of the homogeneous field amplitude, normalized to $\chi_*$ (cf. \ref{['chistardef']}), as a function of the number of $e$-folds since the onset of RD, $N\equiv\ln(a/a_*)=\ln(1+z/\nu)$ for different values of the bare mass $M$, obtained from numerically solving Eq. \ref{['eq:KG_Y_NoGradient']}. The parameters are fixed to $H_*=\Lambda=10^{12}\,\mathrm{GeV}$ with a fiducial initial condition $Y(0)=10^{-3}$. Black squares indicate the symmetry restoration time $z_{\rm sr}$ at which the effective squared mass \ref{['eq:mass']} changes sign.
• Figure 3: Evolution of the homogeneous energy density of the DM field as a function of the number of $e$-folds since the onset of RD, $N\equiv\ln(a/a_*)=\ln(1+z/\nu)$, for different values of the bare mass $M$, computed from Eq. \ref{['eq:chi_en']} and normalized to the critical density $\rho_{\rm crit}=3M_P^2H_\ast^2$. The parameters are fixed to $H_*=\Lambda=10^{12}\,\mathrm{GeV}$ with initial condition $Y(0)=10^{-3}$. The red and black dashed lines indicate, respectively, the reference scalings $\rho\propto a^{-3}$ characteristic of pressureless matter and $\rho\propto a^{-4}$ characteristic of radiation
• Figure 4: Evolution of the mode amplitudes $|f_\kappa(z)|$ at $N=0.25, 0.5 ,1,$ and $2$$e$-folds since the onset of RD, for $\Lambda=H_*$. The black horizontal line marks unit normalization. IR modes at low $\kappa$ exhibit pronounced amplification, reflecting the tachyonic growth induced by the curvature-driven instability.
• Figure 5: Evolution of the dimensionless power spectrum $\kappa^{3}\lvert f_\kappa(z)\rvert^{2}$ during the tachyonic phase for several times $z=5$--$13$, $\Lambda=H_*$ and $M=10^9$ GeV. Solid curves correspond to the analytical approximation \ref{['spectrumapp']} based on the uniform WKB treatment, while dashed curves show the full numerical solution of the mode equation \ref{['eq:quantum_freq']}. The spectrum is dominated by IR modes and exhibits a pronounced peak at $\kappa\simeq\kappa_*$, whose amplitude grows rapidly with time.