Gravitational waves from supercooled phase transitions and pulsar timing array signals

The recent detection of a gravitational wave background in the nano-Hertz frequency range by Pulsar Timing Array (PTA) collaborations, including NANOGrav, EPTA, and PPTA, has opened a new avenue for exploring fundamental physics in the early universe. In this work, we analyze a supercooled first-order phase transition in a hidden sector with a spontaneously broken $U(1)_X$ gauge symmetry as a source for this signal. We demonstrate that the thermal history of the hidden and visible sectors plays a crucial role in the gravitational wave power spectrum analysis. Our analysis shows that supercooled phase transitions can generate gravitational waves strong enough to explain the PTA observations while satisfying cosmological constraints from Big Bang Nucleosynthesis.