  Recently, the NANOGrav, PPTA, EPTA, and CPTA collaborations independently
reported their evidence of the Stochastic Gravitational Waves Background
(SGWB). While the inferred gravitational-wave background amplitude and spectrum
are consistent with astrophysical expectations for a signal from the population
of supermassive black-hole binaries (SMBHBs), the search for new physics
remains plausible in this observational window. In this work, we explore the
possibility of explaining such a signal by the scalar-induced gravitational
waves (IGWs) in the very early universe. We use a parameterized broken
power-law function as a general description of the energy spectrum of the SGWB
and fit it to the new results of NANOGrav, PPTA and EPTA. We find that this
approach can put constraints on the parameters of IGW energy spectrum and
further yield restrictions on various inflation models that may produce
primordial black holes (PBHs) in the early universe, which is also expected to
be examined by the forthcoming space-based GW experiments.
