When the Universe Expands Too Fast: Relentless Dark Matter

We consider a modification to the standard cosmological history consisting of introducing a new species $φ$ whose energy density red-shifts with the scale factor $a$ like $ρ_φ\propto a^{-(4+n)}$. For $n>0$, such a red-shift is faster than radiation, hence the new species dominates the energy budget of the universe at early times while it is completely negligible at late times. If equality with the radiation energy density is achieved at low enough temperatures, dark matter can be produced as a thermal relic during the new cosmological phase. Dark matter freeze-out then occurs at higher temperatures compared to the standard case, implying that reproducing the observed abundance requires significantly larger annihilation rates. Here, we point out a completely new phenomenon, which we refer to as $\textit{relentless}$ dark matter: for large enough $n$, unlike the standard case where annihilation ends shortly after the departure from thermal equilibrium, dark matter particles keep annihilating long after leaving chemical equilibrium, with a significant depletion of the final relic abundance. Relentless annihilation occurs for $n \geq 2$ and $n \geq 4$ for s-wave and p-wave annihilation, respectively, and it thus occurs in well motivated scenarios such as a quintessence with a kination phase. We discuss a few microscopic realizations for the new cosmological component and highlight the phenomenological consequences of our calculations for dark matter searches.