Purely gravitational dark matter production in warm inflation

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 $\rho_\chi\propto m_\chi^{1/2}(m_\chi^{5/2})$ 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.