Constraining Cosmological Phase Transitions with the Parkes Pulsar Timing Array

A cosmological first-order phase transition is expected to produce a stochastic gravitational wave background. If the phase transition temperature is on the MeV scale, the power spectrum of the induced stochastic gravitational waves peaks around nanohertz frequencies, and can thus be probed with high-precision pulsar timing observations. We search for such a stochastic gravitational wave background with the latest data set of the Parkes Pulsar Timing Array. We find no evidence for a Hellings-Downs spatial correlation as expected for a stochastic gravitational wave background. Therefore, we present constraints on first-order phase transition model parameters. Our analysis shows that pulsar timing is particularly sensitive to the low-temperature ($T\sim 1–100\mathrm{MeV}$) phase transition with a duration $(\beta /H_{*}{)}^{-1}\sim {10}^{-2}-{10}^{-1}$ and therefore can be used to constrain the dark and QCD phase transitions.

Figure 1

The 95% credibility Bayesian upper limits on the energy density of a free-spectrum SGWB based on the PPTA data. The solid, dotted, and dashed black curves indicate results under different assumptions (hypotheses $H2$, $H3$, and $H4$ in Table 1, respectively, where the FOPT spectrum is substituted with the free spectrum). The region excluded by BBN [69] is shaded gray. Red curves with filled markers show examples of the spectrum predicted in the FOPT model, with $(\beta /H_{*}{)}^{-1}=0.1$, and varying parameters $(\alpha ,T_{*})=\{(0.2,3\mathrm{MeV})(\mathrm{circle}),(0.5,3\mathrm{MeV})(\mathrm{triangle}),(0.5,30\mathrm{MeV})(\mathrm{square})\}$, respectively.

Figure 2

The PPTA exclusion contours (at 95% C.L.) on FOPT parameters ${\log }_{10}(T_{*}/\mathrm{GeV})$ and ${\log }_{10}[(\beta /H_{*}{)}^{-1}]$, for $\alpha =0.2$, 0.5, and 1.0.