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Recently, several major pulsar timing array (PTA) collaborations haveassembled strong evidence for the existence of a gravitational-wave backgroundat frequencies around the nanohertz regime. Assuming that the PTA signal isattributed to scalar-induced gravitational waves, we jointly employ the PTAdata from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe theconditions of the early Universe. Specifically, we explore the equation ofstate parameter ($w$), the sound speed ($c_s$), and the reheating temperature($T_\mathrm{rh}$), finding $w=0.60^{+0.32}_{-0.39}$, $c_s\gtrsim 0.09$, and$T_\mathrm{rh}\lesssim 0.2\,\mathrm{GeV}$ for a lognormal power spectrum of thecurvature perturbation. Furthermore, we compute Bayes factors to comparedifferent models against the radiation domination model ($c_s^2 = w = 1/3$),effectively excluding the pressure-less fluid domination model. Our studyunderscores the significance of scalar-induced gravitational waves as apowerful tool to explore the nature of the early Universe.

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays