Pitfalls of a power-law parameterization of the primordial power spectrum for Primordial Black Hole formation

TL;DR

Using a power-law model to estimate primordial fluctuations for PBH formation often results in significant errors, making abundance predictions unreliable.

Contribution

This paper demonstrates that the common power-law parameterization introduces large inaccuracies in small-scale fluctuation amplitudes relevant for PBH formation.

Findings

Power-law extrapolation causes large errors in small-scale amplitude estimates.

Inaccurate amplitude predictions lead to unreliable PBH abundance calculations.

The study highlights the need for more precise models for primordial power spectra.

Abstract

Primordial Black Holes (PBHs) can form in the radiation dominated early Universe from the collapse of large density perturbations produced by inflation. A power-law parameterisation of the primordial power spectrum is often used to extrapolate from cosmological scales, where the amplitude of the perturbations is well-measured by Cosmic Microwave Background and Large Scale Structure observations, down to the small scales on which PBHs may form. We show that this typically leads to large errors in the amplitude of the fluctuations on small scales, and hence extremely inaccurate calculations of the abundance of PBHs formed.