Cosmology of self-interacting ultralight dark matter: simultaneous shifts in the Hubble constant and structure growth

We study the cosmology of self-interacting ultralight dark matter. The scalar field evolves from an early Hubble-frozen phase to a quartic-dominated radiation-like phase and finally to a quadratic matter-like phase. The intermediate phase increases the pre-recombination expansion rate and reduces the sound horizon, while the late phase allows the same field to contribute to dark matter. We implement the background and linear perturbations of a mixed cold-dark-matter and ultralight-dark-matter cosmology in CLASS. For $m={10}^{-22}\mathrm{e}\mathrm{V}$ and $\tilde{m}\simeq 1\mathrm{e}\mathrm{V}$, increasing the ultralight-dark-matter fraction raises the fixed-${\theta }_{\ast }$ value of $H_0$, lowers the late-time clustering amplitude, strengthens the scale-dependent matter-power suppression, and produces a smooth CMB-temperature residual reaching about $9\mathrm{\%}$ for the largest fraction considered. The model therefore generates simultaneous background and growth shifts in the directions relevant to the Hubble and structure-growth tensions. Establishing whether these shifts improve a joint fit requires a likelihood-level observational analysis.