Gravitational ultra-relativistic freeze-out during general reheating

Abstract

We investigate ultrarelativistic freeze-out (UFO) in the context of generic reheating scenarios. While the standard WIMP dark matter paradigm has been extensively studied, UFO has so far only been analyzed within the specific reheating channel $\phi \rightarrow f\bar{f}$. Unlike in the standard WIMP mechanism, where dark matter can only be diluted after freeze-out at $T_\mathrm{FO} \sim m_\chi/\mathcal{O}(10)$, UFO dark matter can undergo freeze-in like phases following the initial freeze-out, driven by the non-trivial temperature evolution. The exact temperature evolution then needs to be accounted for, as a change in the temperature scaling can modify the IR/UV nature of UFO, impacting the relic abundance. We first generalize UFO to an arbitrary temperature profile $T \sim a^{-\xi}$, making explicit the UV and IR regimes for a thermally averaged cross section $\langle \sigma v \rangle \sim T^n / \Lambda^{n+2}$. Then, as a concrete example, we consider the minimal scenario in which gravitational particle production at the onset of reheating sources an initial radiation abundance, and show that this early hot bath changes the UFO parameter space. We refer to this effect as GUFO. Specializing to $n = 2$, we find that matter-like reheating ($V \sim \phi^2$) accommodates dark matter masses up to $10^7~\mathrm{GeV}$ for $\Lambda \lesssim 10^9~\mathrm{GeV}$ as thermalization becomes less stringent, while radiation-like reheating ($V \sim \phi^4$) is compatible with GUFO across all reheating channels only if gravitational processes are taken into account.