Constraints on Primordial Black Holes from N_eff: Scalar-induced Gravitational Waves as an Extra Radiation Component

Abstract In 2023 June, multiple pulsar timing array collaborations provided evidence for the existence of a stochastic gravitational-wave background. Scalar-induced gravitational waves (SIGWs), as one of the most likely sources of stochastic gravitational waves, have received widespread attention. When primordial curvature perturbations on small scales are sufficiently large, primordial black holes (PBHs) inevitably form, concurrently producing SIGWs with significant observable effects. These SIGWs can serve as an additional radiation component, influencing the relativistic degrees of freedom N eff . Taking into account primordial non-Gaussianity, we study the energy density spectrum of SIGWs up to the third order and use the current observational data of N eff to constrain small-scale primordial curvature perturbations and the abundance of PBHs.