Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays
Lang Liü, You Wu, Zu-Cheng Chen
Abstract
Abstract Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter ( w ), the reheating temperature ( T rh ), and the sound speed ( c s ), finding w = 0.59 +0.36 -0.40 (median + 90% credible interval), and T rh ≲ 0.2 GeV at the 95% credible interval for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the power-law spectrum model, effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.