Stepped Partially Acoustic Dark Matter, Large Scale Structure, and the Hubble Tension

We propose a new interacting dark sector model, Stepped Partially Acoustic Dark Matter (SPartAcous), that can simultaneously address the two most important tensions in current cosmological data, the $H_0$ and $S_8$ problems. As in the Partially Acoustic Dark Matter (PAcDM) scenario, this model features a subcomponent of dark matter that interacts with dark radiation at high temperatures, suppressing the growth of structure at small scales and thereby addressing the $S_8$ problem. However, in the SPartAcous model, the dark radiation includes a component with a light mass that becomes non-relativistic close to the time of matter-radiation equality. As this light component annihilates away, the remaining dark radiation heats up and its interactions with dark matter decouple. The heating up of the dark sector results in a step-like increase in the relative energy density in dark radiation, significantly reducing the $H_0$ tension, while the decoupling of dark matter and dark radiation ensures that the power spectrum at larger scales is identical to $\Lambda$CDM.