Squeezing Cosmological Phase Transitions with International Pulsar Timing Array

TL;DR

This study uses recent pulsar timing array data to constrain the properties of early universe phase transitions, providing tighter bounds on transition temperature, duration, and strength, and revealing correlations among parameters.

Contribution

It introduces a comprehensive analysis of phase transition parameters using pulsar timing data, including free spectral shape parameters, and establishes the first constraint on the spectral shape parameter a.

Findings

Dark or QCD phase transitions below 66 MeV are ruled out at 2σ.

Tighter bounds on transition duration, strength, and friction compared to previous NANOGrav results.

First constraint on the spectral shape parameter a, indicating pulsar timing's sensitivity to this parameter.

Abstract

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.