Constraints On Scalar-Induced Gravitational Waves Up To Third Order From 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 (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 $A_{\zeta }\gtrsim 0.06$. 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.

arXiv comment10 pages, 2 columns, 3 figures. Version accepted by Physical Review Research

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