The process of \acp{PBH} formation would be inevitably accompanied by \acp{SIGW}. This strong correlation between \acp{PBH} and \acp{SIGW} signals could be a promising approach to detecting \acp{PBH} in the upcoming \ac{GW} experiments, such as \ac{LISA}. We investigate the third order \acp{SIGW} during a \ac{RD} era in the case of a monochromatic primordial power spectrum Pζ=Aζk∗δ(k−k∗). For \ac{LISA} observations, the relations between \ac{SNR} and monochromatic primordial power spectrum are studied systematically. It shows that the effects of third order \acp{SIGW} extend the cutoff frequency from 2f∗ to 3f∗ and lead to about 200% increase of the \ac{SNR} for frequency band from 10−5Hz to 1.6×10−3Hz corresponding to \acp{PBH} with mass range 4×10−12M⊙∼10−7M⊙. We find that there exists a critical value A∗=1.76×10−2 for the amplitude of the monochromatic primordial power spectra, such that when Aζ>A∗, the energy density of third order \acp{SIGW} will be larger than the energy density of second order \acp{SIGW}.
@article{arxiv.2209.12404,
title = {Primordial black holes and third order scalar induced gravitational waves},
author = {Zhe Chang and Yu-Ting Kuang and Xukun Zhang and Jing-Zhi Zhou},
journal= {arXiv preprint arXiv:2209.12404},
year = {2023}
}