The curvature perturbations and induced gravitational waves induced by the first-order phase transition during reheating

We propose a novel mechanism where a first-order phase transition modulates the decay rate of a massive field. This modulation, even if the scalar field has negligible energy density, subsequently generates an observable stochastic gravitational-wave background. The stochastic nature of bubble nucleation leads to the asynchrony of phase transitions, generating superhorizon-scale density perturbations through spatial variations in the decay rate $\mathrm{\Gamma }$. These perturbations subsequently source second-order gravitational waves with peak amplitudes governed by the phase transition parameter $\beta \mathrm{/}{H}_{\ast }$ and decay rate $\mathrm{\Gamma }$. We apply this mechanism in the reheating scanario where the decay rate of inflaton are modulated by the scalar field that undergoes a first-order phase transition. Numerical calculations reveal that the gravitational wave energy spectrum typically reaches ${\mathrm{\Omega }}_{\text{GW}}\sim {10}^{-10}$, demonstrating prospects for detection by space-based interferometers like LISA, TianQin and Taiji. This work establishes a new approach to probe phase transition processes in the early Universe without requiring significant vacuum energy release.