Partial Relief of the Hubble Tension and a Natural Self-Interacting Dark Matter Candidate From Staged Symmetry Breaking

The values of the Hubble constant (${\mathrm{H}}_0$) inferred from the cosmic microwave background (CMB) and local measurements via the distance ladder exhibit a $\sim 5\sigma$ 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, so that the equation of state parameter of the subcomponent shifts from $w\approx 0$ at early times to $w\approx -1\mathrm{/}3$ at late times. We provide an effective field theory whose structure is partially motivated by the desire for a plausible UV completion. We find that such a construction naturally produces a possible self-interacting dark matter candidate with a velocity-dependent scattering cross section as a by-product of gauge invariance. This is relevant for addressing tensions between the predictions of $\mathrm{\Lambda }$CDM and observations of small-scale structure, such as the core-cusp problem.