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We perform a Bayesian search in the latest Pulsar Timing Array (PTA) datasetsfor a stochastic gravitational wave (GW) background sourced by curvatureperturbations at scales $10^5~\text{Mpc}^{-1}\lesssim k\lesssim10^8~\text{Mpc}^{-1}$. These re-enter the Hubble horizon at temperatures aroundand below the QCD crossover phase transition in the early Universe. We includea stochastic background of astrophysical origin in our search and properlyaccount for constraints on the curvature power spectrum from the overproductionof primordial black holes (PBHs). We find that the International PTA DataRelease 2 significantly favors the astrophysical model for its reportedcommon-spectrum process, over the curvature-induced background. On the otherhand, the two interpretations fit the NANOgrav 12.5 years dataset equally well.We then set new upper limits on the amplitude of the curvature power spectrumat small scales. These are independent from, and competitive with, indirectastrophysical bounds from the abundance of PBH dark matter. Upcoming PTA datareleases will provide the strongest probe of the curvature power spectrumaround the QCD epoch.

Search for scalar induced gravitational waves in the International Pulsar Timing Array Data Release 2 and NANOgrav 12.5 years datasets