Reconstruction of Primordial Power Spectrum from Gravitational Waves of High-Redshift Black Hole Binaries

Abstract

High-redshift binary black hole (BBH) events are promising candidates for primordial black holes (PBHs) detectable by next-generation gravitational wave (GW) detectors. A redshifted mass distribution of detected PBH candidates can be obtained from GW observations, from which the underlying PBH mass function can be reconstructed. In this work, we develop a framework that applies the gradient-descent method to the observed redshifted mass distribution and reconstructs the PBH mass function and, subsequently, the primordial power spectrum (PPS) on small scales. As an illustrative application, we analyze BBH events in the LIGO--Virgo--KAGRA (LVK) catalogs under a specified PBH selection criterion. We find a regularization-stable candidate bump-like enhancement of order $\mathcal{O}(10^{-2})$ in the reconstructed PPS, centered around $k_{\mathrm{peak}}\simeq 5.7\times 10^5~\mathrm{Mpc}^{-1}$ under the adopted assumptions. Our results demonstrate the feasibility of reconstructing the small-scale PPS from high-redshift BBH observations with next-generation GW detectors.