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Abstract The recently released data by pulsar timing array (PTA) collaborations have amassed substantial evidence corroborating the existence of a stochastic signal consistent with a gravitational-wave background at frequencies around the nanohertz regime. We investigate the situation in which the PTA signal originates from scalar-induced gravitational waves (SIGWs), which serves as a valuable tool to probe the equation of state parameter w during the Universe's early stages. The joint consideration of the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 yields that w = 0.60 +0.32 -0.39 (median + 90% credible interval), indicating a period of condensate domination at the production of SIGWs is allowed by the data. Moreover, the data also supports radiation domination ( w = 1/3) within the 90% credible interval. We also impose an upper bound on the reheating temperature that T rh ≲ 0.2 GeV and the constraint on w reveals valuable information on the inflationary potential and the dynamics at the end of inflation.
Liü et al. (Wed,) studied this question.