Constraints On Scalar-Induced Gravitational Waves Up To Third Order From 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 (PTA). In the framework of scalar-induced gravitational waves (SIGWs), we concurrently investigate the second and third order gravitational waves by jointly analyzing PTA data, alongside big-bang nucleosynthesis (BBN), and cosmic microwave background (CMB) datasets. We determine the primordial curvature spectral amplitude as $0.021<A_\zeta<0.085$ and the spectral peak frequency as $10^{-7.3}\ \mathrm{Hz}<f_\ast<10^{-6.3}\ \mathrm{Hz}$ at a 95\% confidence interval, pointing towards a mass range for primordial black holes of $10^{-4.5}M_\odot<m_{\mathrm{PBH}}<10^{-2.5}M_\odot$. Our findings suggest that third order gravitational waves contribute more significantly to the integrated energy density than the second order ones when $A_\zeta\gtrsim0.06$. 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.