Supercooled Phase Transitions: Why Thermal History of Hidden Sector Matters in Analysis of Pulsar Timing Array Signals

The detection of a gravitational wave background in the nano-Hertz frequency range from Pulsar Timing Array (PTA) observations offers new insights into evolution of the early universe. In this work we analyze gravitational wave data from PPTA, EPTA, and NANOGrav, as arising from a supercooled first-order phase transition within a hidden sector, characterized by a broken $U(1)_X$ gauge symmetry. Several previous works have discussed challenges in producing observable {PTA signal} from supercooled phases transitions. We discuss these challenges and show how they are overcome by inclusion in part of the proper thermal history of the hidden and the visible sectors. The analysis of this work demonstrates that thermal histories of hidden and visible sectors profoundly influence the gravitational wave power spectrum, an aspect not previously explored in the literature. Further, the analysis of this work suggests that supercooled phase transitions not only align with the Pulsar Timing Array observations but also show promise for gravitational wave detection by future gravitational wave detectors. Our analysis shows that the dominant contribution to the gravitational wave power spectrum for PTA signals comes from bubble collision while the sound wave and turbulence contributions are highly suppressed. It is also found that all the PTA events are of detonation type while deflagration and hybrid events are absent. The analysis presented in this work provides a robust framework for further investigations on the origin of gravitational wave power spectrum in the early universe and for their experimental observation in the future.