Towards a reliable reconstruction of the power spectrum of primordial curvature perturbation on small scales from GWTC-3

Primordial black holes (PBHs) can be both candidates of dark matter and progenitors of binary black holes (BBHs) detected by the LIGO-Virgo-KAGRA collaboration. Since PBHs could form in the very early Universe through the gravitational collapse of primordial density perturbations, the population of BBHs detected by gravitational waves encodes much information on primordial curvature perturbation. In this work, we take a reliable and systematic approach to reconstruct the power spectrum of the primordial curvature perturbation from GWTC-3, under the hierarchical Bayesian inference framework, by accounting for the measurement uncertainties and selection effects. In addition to just considering the single PBH population model, we also report the results considering the multi-population model, i.e., the mixed PBH and astrophysical black hole binaries model. We find that the maximum amplitude of the reconstructed power spectrum of primordial curvature perturbation can be $\sim2.5\times10^{-2}$ at $\mathcal{O}(10^{5})~\rm Mpc^{-1}$ scales, which is consistent with the PBH formation scenario from inflation at small scales.