Primordial black holes and uncertainties in the choice of the window\n function

Abstract

Primordial black holes (PBHs) can be produced by the perturbations that exit\nthe horizon during inflationary phase. While inflation models predict the power\nspectrum of the perturbations in Fourier space, the PBH abundance depends on\nthe probability distribution function (PDF) of density perturbations in real\nspace. In order to estimate the PBH abundance in a given inflation model, we\nmust relate the power spectrum in Fourier space to the PDF in real space by\ncoarse-graining the perturbations with a window function. However, there are\nuncertainties on what window function should be used, which could change the\nrelation between the PBH abundance and the power spectrum. This is particularly\nimportant in considering PBHs with mass $30 M_\\odot$ that account for the LIGO\nevents because the required power spectrum is severely constrained by the\nobservations. In this paper, we investigate how large influence the\nuncertainties on the choice of a window function have over the power spectrum\nrequired for LIGO PBHs. As a result, it is found that the uncertainties\nsignificantly affect the prediction for the stochastic gravitational waves\n(GWs) induced by the second order effect of the perturbations. In particular,\nthe pulsar timing array constraints on the produced GWs could disappear for the\nreal-space top-hat window function.\n