Squeezing Cosmological Phase Transitions with International Pulsar
  Timing Array
  A first-order MeV-scale cosmological phase transition (PT) can generate a
peak in the power spectrum of stochastic gravitational wave background around
nanohertz frequencies. With the recent International Pulsar Timing Array data
release two covering nanohertz frequencies, we search for such a phase
transition signal. For the standard 4-parameter PT model, we obtain the PT
temperature $T_\star\in$ [66 MeV, 30 GeV], which indicates that dark or QCD
phase transitions occurring below 66 MeV have been ruled out at $2\,\sigma$
confidence level. This constraint is much tighter than $T_\star\sim$ [1 MeV,
100 GeV] from NANOGrav. We also give much tighter $2\,\sigma$ bounds on the PT
duration $H_\star/\beta>0.1$, strength $\alpha_\star>0.39$ and friction
$\eta<2.74$ than NANOGrav. For the first time, we find a positive correlation
between $\mathrm{log}_{10}T_\star$ and $\mathrm{log}_{10}H_\star/\beta$
implying that PT temperature increases with increasing bubble nucleation rate.
To avoid large theoretical uncertainties in calculating PT spectrum, we make
bubble spectral shape parameters $a$, $b$, $c$ and four PT parameters free
together, and confront this model with data. We find that pulsar timing is very
sensitive to the parameter $a$, and give the first clear constraint
$a=1.27_{-0.54}^{+0.71}$ at $1\,\sigma$ confidence level.
