Purely gravitational dark matter production in warm inflation

TL;DR

This work explores purely gravitational dark matter production in warm inflation (WI), focusing on three channels: CGPP, graviton-mediated SM annihilation, and inflaton annihilation. WI alters production thermodynamics, notably suppressing sub-inflaton-mass DM from inflaton annihilation and introducing a minimum end-of-WI temperature $T_e$ required for adequate relic density, while CGPP yields distinct abundance-mass scalings $\rho_\chi \propto m_\chi^{1/2}$ (minimal) and $\rho_\chi \propto m_\chi^{5/2}$ (conformal). The study derives analytic yields, identifies mass windows (roughly $m_\chi \in [10^{-8},10^{-2}] M_P$ for minimal coupling and $[10^{-14},10^{-2}] M_P$ for conformal coupling), and applies isocurvature and Lyman-$\alpha$ constraints to bound the viable parameter space. These results link WI’s thermal history to gravitational DM production, offering a potential route to distinguish WI from standard inflation via future observations of DM mass and primordial gravitational waves. The framework generalizes to fermionic and vector DM and highlights how end-of-inflation temperature and gravitational interactions shape DM genesis in the early universe.

Abstract

We consider an appealing scenario for the production of purely gravitational dark matter in the background of warm inflation, a mechanism that maintains stable thermal bath during inflation. Through systematic investigation of various gravitational production channels, we reveal distinctive features compared to the standard inflation scenario. Notably, the inflaton annihilation channel in warm inflation exhibits markedly different thermodynamics from the standard inflation paradigm, leading to a suppression on the production of sub-inflaton-mass dark matter. For the production channel of inflationary vacuum fluctuations, we find an abundance-mass correlation of $ρ_χ\propto m_χ^{1/2}(m_χ^{5/2})$ for the sub-Hubble-mass dark matter with minimal(conformal) coupling. Our results also indicate that a minimum temperature threshold of $10^{-6}M_P$ is necessary for warm inflation, which allows adequate dark matter production. With observational constraints, our results provide stringent limits on the mass range of purely gravitational dark matter with sufficient density: $10^{-8}-10^{-2}M_P$ for minimal coupling and $10^{-14}-10^{-2}M_P$ for conformal coupling.

Figures (6)

• Figure 1: Evolution of various dimensionless quantities during the late stage of WI. The inflationary potential is assumed to possess a $\phi^2$ bottom with $m_\phi=10^{-5}M_P$. In the left panel we set $p=0$, $c=1$, and $C_\Upsilon=0.1(10)$ for the solid(dashed) curves. In the right panel we set $p=0$, $c=-1$, and $C_\Upsilon=2\times10^{-8}(2\times10^{-7})$ for the solid(dashed) curves. The end of WI is fixed at $N=0$.
• Figure 2: Illustration of the $s$-channel graviton-mediated annihilation process. The initial and final state are labeled by $i$ and $f$. Arrows mean the directions of momenta.
• Figure 3: DM yield via gravitational annihilation during and after WI (red curves) and SI with reheating (blue curves). The inflationary potential is assumed to possess a $\phi^2$ bottom with $m_\phi=10^{-5}M_P$. For WI, we set $p=0$, $c=1$, and $C_\Upsilon=0.1$. The radiation temperature is $T_e=5\times10^{-4}M_P$ at the end of WI. For SI, we set the reheating efficiency $\Gamma=0.1H_e=6.5\times10^{-7}M_P$. The max temperature during reheating is $T_\mathrm{max}=5\times10^{-4}M_P$. The initial state is set as the average of all SM particles, and the DM is considered as a real scalar with mass of $m_\chi=0.1T_e,~T_e,~5T_e$ respectively. The end of WI is fixed at $N=0$.
• Figure 4: Relic abundance of scalar DM produced by the gravitational annihilation of SM particles (red curves) and inflatons (blue curves). We have assumed $m_\phi\ll T_e$.
• Figure 5: Relic abundance of scalar DM with minimal (red curves) and conformal (blue curves) coupling via CGPP mechanism in WI. The inflationary background is served by a $\phi^2$ WI model. We set $m_\phi=10^{-5}(10^{-7})M_P$, $T_e=5\times10^{-4}(5\times10^{-5})M_P$, and $H_e=10^{-6}(10^{-8})M_P$ for the solid(dashed) curves. For comparison, the gray dashed curves depict DM relic abundance in the $\phi^2$ SI scenario with $m_\phi=10^{-5}M_P$ and $T_\mathrm{reh}=3\times10^{-5}M_P$.