Phase Transitions and Gravitational Wave Production at the End of Thermal Inflation

We investigate the first-order phase transition that terminates thermal inflation and evaluate the associated stochastic gravitational-wave signals. The transition is first characterized through semi-analytic calculations of the bounce action, which are compared with numerical results obtained using CosmoTransitions. We then study its real-time evolution in a three-dimensional Langevin lattice simulation that incorporates Hubble expansion and the corresponding temperature evolution throughout the transition. The lattice dynamics are consistent with the bounce-action estimates: the transition proceeds through localized bubble nucleation and subsequent bubble growth, rather than through a phase-mixing instability. Using the resulting transition parameters, we estimate the gravitational-wave spectra generated by bubble collisions and acoustic motions in the plasma. The predicted stochastic background lies within the projected sensitivity ranges of future gravitational-wave observatories, including BBO and DECIGO.