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

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 0.021Aζ0.085 and the spectral peak frequency as 10−7.3Hzf*10−6.3Hz at a 95% confidence interval, pointing towards a mass range for primordial black holes of 10−4.5M⊙mPBH10−2.5M⊙. Our findings suggest that third-order gravitational waves contribute more significantly to the integrated energy density than the second-order ones when Aζ≳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. Published by the American Physical Society 2024