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 ${10}^{-7.3}\mathrm{H}\mathrm{z}<f_{\ast }<{10}^{-6.3}\mathrm{H}\mathrm{z}$ at a 95% confidence interval, pointing towards a mass range for primordial black holes of ${10}^{-4.5}{M}_{\odot }<m_{\mathrm{P}\mathrm{B}\mathrm{H}}<{10}^{-2.5}{M}_{\odot }$. Our findings suggest that third order gravitational waves contribute more significantly to the integrated energy density than the second order ones when $A_{\zeta }\gtrsim 0.06$. 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.