Lawrence Berkeley National Laboratory

We consider first order cosmological phase transitions (PTs) happening at late times below standard model temperatures T_{PT}≲GeV. The inherently stochastic nature of bubble nucleation and the finite number of bubbles associated with a late-time PT lead to superhorizon fluctuations in the PT completion time. We compute how such fluctuations eventually source curvature fluctuations with universal properties, independent of the microphysics of the PT dynamics. Using cosmic microwave background (CMB) and large scale structure measurements, we constrain the energy released in a dark-sector PT. For 0.1  eV≲T_{PT}≲keV this constraint is stronger than both the current bound from additional neutrino species ΔN_{eff}, and in some cases, even CMB-S4 projections. Future measurements of CMB spectral distortions and pulsar timing arrays will also provide competitive sensitivity for keV≲T_{PT}≲GeV.