| Summary: | Abstract The LIGO observatories can potentially detect stochastic gravitational waves arising from phase transitions which happened in the early universe at temperatures around T ∼ 108 GeV. This provides an extraordinary opportunity for discovering the phase transition associated with the breaking of the Peccei-Quinn symmetry, required in QCD axion models. Here we consider the simplest Peccei-Quinn models and study under which conditions a strong first-order phase transition can occur, analyzing its associated gravitational wave signal. To be detectable at LIGO, we show that some supercooling is needed, which can arise either in Coleman-Weinberg-type symmetry breaking or in strongly-coupled models. We also investigate phase transitions that interestingly proceed by first breaking the electroweak symmetry at large scales before tunneling to the Peccei-Quinn breaking vacuum. In this case, the associated gravitational wave signal is more likely to be probed at the proposed Einstein Telescope.
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