Imprints of Early Universe Cosmology on Gravitational Waves

Abstract: We explore the potential of gravitational waves (GWs) to probe the pre-BBN era of the early universe, focusing on the effects of energy injection. Specifically, we examine a hidden sector alongside the Standard Model that undergoes a strong first-order phase transition (FOPT), producing a GW signal. Once the phase transition has completed, energy injection initiates reheating in the hidden sector, which positions the hidden sector field so that additional phase transitions can occur. This can result in a total of three distinct phase transitions with a unique three-peak GW spectrum. Among these transitions, the first and third are of the standard type, while the intermediate second transition is inverted, moving from a broken to an unbroken phase. Using polynomial potentials as a framework, we derive analytical relations among the phase transition parameters and the resulting GW spectrum. Our results indicate that the second and third transitions generate GWs with higher amplitudes than the first, with a peak frequency ratio differing by up to an order of magnitude. This three-peak GW spectrum is detectable by upcoming facilities such as LISA, BBO, and UDECIGO. Notably, the phenomenon is robust across various potentials and model parameters, suggesting that hidden sector GWs provide a powerful tool for exploring new physics scenarios in the pre-BBN era.