Reconstruction of Power Spectrum of Primordial Curvature Perturbations on small scales from Primordial Black Hole Binaries scenario of LIGO/VIRGO detection

As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to $\mathcal{O}({10}^{-2})$ on scales $\mathcal{O}(1)$ pc. This may imply the validity of PBH as a possible BBH merger candidate.