Impact of cosmic expansion on gravitational wave spectra from strongly supercooled first-order phase transitions

We study gravitational wave production from strongly supercooled first-order phase transitions while consistently tracking the evolution of the cosmological background. Our analysis includes the reheating process that ends the period of thermal inflation and restores radiation domination. We find that this background evolution leaves the spectral shape largely intact, except for a causality-driven tail on super-horizon scales. However, for sufficiently slow transitions, the peak amplitude and frequency exhibit a weaker dependence on the transition rate β than the usual scaling of ∝ β − 2 and ∝ β , respectively.