Quasidecoupled state for dark matter in nonstandard thermal histories

Dark matter drops out of kinetic equilibrium with standard model particles when the momentum-transfer rate equals the expansion rate. In a radiation-dominated universe, this occurs at essentially the same time as dark matter kinetically decouples from the plasma. Dark matter may also fall out of kinetic equilibrium with standard model particles during an early matter-dominated era (EMDE), which occurs when the energy content of the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before big bang nucleosynthesis. Until now, it has been assumed that kinetic decoupling during an EMDE happens similarly to the way it does in a radiation-dominated era. We show that this is not the case. By studying the evolution of the dark matter temperature, we establish a quasidecoupled state for dark matter in an EMDE, during which the dark matter temperature cools faster than the plasma temperature but slower than it would cool if the dark matter were fully decoupled. The dark matter does not fully decouple until the EMDE ends and the Universe becomes radiation dominated. We also extend the criteria for quasidecoupling to other nonstandard thermal histories and consider how quasidecoupling affects the free-streaming length of dark matter.