Partial relief of the Hubble tension and a natural self-interacting dark matter candidate from staged symmetry breaking

The values of the Hubble constant ($\rm{H_0}$) inferred from the cosmic microwave background (CMB) and local measurements via the distance ladder exhibit a $\sim5σ$ tension. In this work we propose that the tension might be partially alleviated if a subcomponent of the dark matter undergoes decays triggered by spontaneous symmetry breaking in the dark sector, where dark energy couples to the daughter species, but not the parent. This then allows interactions between dark matter and dark energy to turn on at a particular redshift, which can reduce fifth-force constraints, since early time interactions are absent. We provide an example of such an effective field theory whose structure is partially motivated by the desire for a plausible UV completion. We find that such a construction can naturally incorporate a possible self-interacting dark matter candidate with a velocity-dependent scattering cross section as a by-product of gauge invariance, though this is not necessary for alleviating the Hubble tension. This is relevant for addressing tensions between $Λ$CDM and small-scale structure, such as the core-cusp problem.