Dark matter cooling during early matter-domination boosts sub-earth halos

Abstract: The existence of an early matter-dominated epoch prior to the Big Bang Nucleosynthesis may lead to a scenario where the thermal dark matter cools faster than plasma before the radiation-dominated era begins. In the radiation-dominated epoch, dark matter free-streams after it decouples both chemically and kinetically from the plasma. In the presence of an early matter-dominated era, chemical decoupling of the dark matter may succeed by a partial kinetic decoupling before reheating ends, depending upon the contributions of different partial wave amplitudes in the elastic scattering rate of the dark matter. We show that the s-wave scattering is sufficient to partially decouple the dark matter from the plasma, if the entropy injection during the reheating era depends on the bath temperature, while p-wave scattering leads to full decoupling in such cosmological backdrop. The decoupling of dark matter before the end of reheating causes an additional amount of cooling, reducing its free-streaming horizon compared to the usual radiation-dominated cosmology. The enhanced matter perturbations for scales entering the horizon prior to the end of reheating, combined with the reduced free-steaming horizon, increase the number density of sub-earth mass halos. The resulting boost in the dark matter annihilation signatures could offer an intriguing probe to differentiate pre-BBN non-standard cosmological epochs. We show that the free-streaming horizon of the dark matter requires to be smaller than a cut-off to ensure a boost in the sub-earth halo populations. As case studies we present two examples: one for a scalar dark matter with $s$-wave elastic scattering and the other one featuring a fermionic dark matter with $p$-wave elastic scattering. We identify regions of parameter space in both models where the dark matter kinetically decouples during reheating, amplifying small-scale structure formation.