Constraints on primordial black holes from $N_{\text{eff}}$ : scalar induced gravitational waves as an extra radiation component

TL;DR

This paper investigates how scalar-induced gravitational waves, generated by primordial curvature perturbations, affect the effective number of relativistic species, providing constraints on primordial black holes and small-scale perturbations.

Contribution

It introduces a third-order energy density spectrum of SIGWs considering primordial non-Gaussianity and uses $N_{\text{eff}}$ data to constrain PBH abundance and curvature perturbations.

Findings

Constraints on small-scale primordial curvature perturbations.

Limits on primordial black hole abundance.

Implications for scalar-induced gravitational wave models.

Abstract

In June 2023, 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, \acp{PBH} inevitably form, concurrently producing SIGWs with significant observable effects. These SIGWs can serve as an additional radiation component, influencing the relativistic degrees of freedom $N_{\text{eff}}$. 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 $N_{\text{eff}}$ to constrain small-scale primordial curvature perturbations and the abundance of \acp{PBH}.