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Recently, the NANOGrav, PPTA, EPTA, and CPTA collaborations independentlyreported their evidence of the Stochastic Gravitational Waves Background(SGWB). While the inferred gravitational-wave background amplitude and spectrumare consistent with astrophysical expectations for a signal from the populationof supermassive black-hole binaries (SMBHBs), the search for new physicsremains plausible in this observational window. In this work, we explore thepossibility of explaining such a signal by the scalar-induced gravitationalwaves (IGWs) in the very early universe. We use a parameterized brokenpower-law function as a general description of the energy spectrum of the SGWBand fit it to the new results of NANOGrav, PPTA and EPTA. We find that thisapproach can put constraints on the parameters of IGW energy spectrum andfurther yield restrictions on various inflation models that may produceprimordial black holes (PBHs) in the early universe, which is also expected tobe examined by the forthcoming space-based GW experiments.

Limits on scalar-induced gravitational waves from the stochastic background by pulsar timing array observations