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    Curvature perturbations and gravitational waves induced by a first-order phase transition during reheating

    Xiao-Bin Sui1,2,3,*, Jing Liu4,5,†, and Rong-Gen Cai6,2,1,‡

    • *Contact author: suixiaobin21@mails.ucas.ac.cn
    • †Contact author: liujing@ucas.ac.cn
    • ‡Contact author: cairg@itp.ac.cn

    Phys. Rev. D 113, 083524 – Published 20 April, 2026

    DOI: https://doi.org/10.1103/26jv-jczj

    Abstract

    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 (GW) 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 Γ. These perturbations subsequently source second-order GWs with peak amplitudes governed by the phase transition parameter β/H* and decay rate Γ. We apply this mechanism in the reheating scenario where the decay rate of the inflaton is modulated by the scalar field that undergoes a first-order phase transition. Numerical calculations reveal that the GW energy spectrum typically reaches ΩGW∼10−10, demonstrating prospects for detection by space-based interferometers like Laser Interferometer Space Antenna, TianQin, and Taiji. This work establishes a new approach to probe phase transition processes in the early Universe without requiring significant vacuum energy release.

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