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Gravitational waves from cosmic strings and first-order phase transition

Cosmic strings and first-order phase transition are two main sources for the stochastic gravitational wave background (SGWB). In this work, we study the stochastic gravitational wave radiation from cosmic string which is formed after the first-order phase transition. For the first-order phase transition occurs at temperature far beyond the electroweak scale, the gravitational wave signal cannot be reached by the future gravitational wave interferometers. The gravitational waves from cosmic strings that formed after the phase transition can be detected by future gravitational wave detectors in a wide range of frequency, and therefore its imprints can serve to search for firs-order phase transitions at high scales with the phase transition temperature: $ \mathcal{O}(10^8)$ GeV $ \leq T_n$ $\leq \mathcal{O}(10^{11})$ GeV.