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Probing scalar induced gravitational waves with PTA and LISA: The Importance of third order correction (2312.14409v2)

Published 22 Dec 2023 in astro-ph.CO and gr-qc

Abstract: We revisit the calculation of third order \acp{SIGW} and extend it from a monochromatic primordial power spectrum to a more general log-normal one. We investigate the impact of third order SIGWs on \ac{SNR} of \ac{LISA} and \ac{PTA} observations, and find that third order SIGWs significantly contribute to the total energy density spectrum of \acp{GW} in high-frequency region. For a primordial power spectrum amplitude of $A_{\zeta}=10{-2}\sim 10{-1}$, the effects of third order SIGWs lead to a $40\%$ to $400\%$ increase in the SNR for LISA. Additionally, our PTA data analysis reveals that third order SIGWs diminish both the amplitude $A_{\zeta}$ and the peak frequency $f_*$ of the primordial power spectrum.

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