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 Aζ=10−2∼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 Aζ and the peak frequency f∗ of the primordial power spectrum.
@article{arxiv.2312.14409,
title = {Probing scalar induced gravitational waves with PTA and LISA: The Importance of third order correction},
author = {Zhe Chang and Yu-Ting Kuang and Di Wu and Jing-Zhi Zhou},
journal= {arXiv preprint arXiv:2312.14409},
year = {2024}
}