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.