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

TL;DR

This paper examines how uncertainties in the choice of window function affect the predicted abundance of primordial black holes and the associated gravitational wave signals, especially for LIGO-mass PBHs.

Contribution

It analyzes the impact of different window functions on PBH abundance estimates and gravitational wave predictions, highlighting the significance of this uncertainty.

Findings

Uncertainties in window functions significantly alter PBH abundance predictions.

The choice of window function can eliminate pulsar timing array constraints on induced GWs.

Predictions for gravitational waves are highly sensitive to the window function used.

Abstract

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