Cosmological and Astrophysical Constraints on Late First-Order Phase Transitions

First-order cosmological phase transitions (PT) can take place in a dark sector at relatively late times between the big-bang nucleosynthesis and recombination epochs. Because bubble nucleation is stochastic, the PT completes at different times in different regions of the Universe. This fluctuation sources a curvature perturbation whose (dimensionless) power spectrum ${\cal P}_\zeta(k)$ features a universal infrared tail, independent of the microscopic details of the PT. Even in the absence of any non-gravitational interaction between the dark sector and the Standard Model, these additional curvature perturbations at small scales impact a variety of observables. We derive new constraints on dark sector phase transitions using {\it Planck}, baryon acoustic oscillation (BAO), Lyman-$\alpha$ observations, spectral distortion limits from FIRAS, constraints on early reionization, and the existence of ultra-faint dwarf galaxies.