Constraints on the Primordial Black Hole Abundance through Scalar-Induced Gravitational Waves from Advanced LIGO and Virgo's First Three Observing Runs

Abstract

As a promising dark matter candidate, primordial black holes (PBHs) lighter than $\sim10^{-18}M_{\odot}$ are supposed to have evaporated by today through Hawking radiation. This scenario is challenged by the memory burden effect, which suggests that the evaporation of black holes may slow down significantly after they have emitted about half of their initial mass. We explore the astrophysical implications of the memory burden effect on the PBH abundance by today and the possibility for PBHs lighter than $\sim10^{-18}M_{\odot}$ to persist as dark matter. Our analysis utilizes current LIGO-Virgo-KAGRA data to constrain the primordial power spectrum and infers the PBH abundance. We find a null detection of scalar-induced gravitational waves that accompanied the formation of the PBHs. Then we place an upper limit on the primordial power spectrum and the PBH abundance to be $f_{\mathrm{pbh}}\simeq0.3$ for PBHs with masses $\sim10^{-24}M_{\odot}$. Furthermore, we expect that next-generation gravitational wave detectors, such as the Einstein Telescope and the Cosmic Explorer, will provide even more stringent constraints. Our results indicate that future detectors can reach sensitivities that could rule out PBH as dark matter within $\sim[10^{-29}M_{\odot},10^{-19}M_{\odot}]$ in the null detection of scalar-induced gravitational waves.