  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 $T_\mathrm{rh} \lesssim 0.2\,\mathrm{GeV}$ and the constraint
on $w$ reveals valuable information on the inflationary potential and the
dynamics at the end of inflation.
