Peccei-Quinn Phase Transition at LIGO
  The LIGO observatories can potentially detect stochastic gravitational waves
arising from phase transitions which happened in the early universe at
temperatures around $T\sim 10^{8}$ 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.
