Constraints on scalar-induced gravitational waves up to third order from a joint analysis of BBN, CMB, and PTA data

Abstract

Recently, strong evidence for a gravitational-wave background has been reported by collaborations of pulsar timing arrays (PTAs). In the framework of scalar-induced gravitational waves, we concurrently investigate the second- and third-order gravitational waves by jointly analyzing PTA data alongside big-bang nucleosynthesis and cosmic microwave background datasets. We determine the primordial curvature spectral amplitude as 0.021<A_{ζ}<0.085 and the spectral peak frequency as 10^{−7.3}Hz<f_{*}<10^{−6.3}Hz at a 95% confidence interval, pointing towards a mass range for primordial black holes of 10^{−4.5}M_{⊙}<m_{PBH}<10^{−2.5}M_{⊙}. Our findings suggest that third-order gravitational waves contribute more significantly to the integrated energy density than the second-order ones when A_{ζ}≳0.06. Furthermore, we expect future PTA projects to validate these findings and provide robust means to investigate the genesis and evolution of the universe, especially inflation.