Generalised constraints on the curvature perturbation from primordial black holes

TL;DR

This paper reviews and updates constraints on primordial black hole abundance to derive limits on the early Universe's curvature perturbations, considering growth of density fluctuations before horizon entry.

Contribution

It provides a comprehensive compilation and update of PBH abundance constraints to refine limits on primordial curvature perturbations across small scales.

Findings

Constraints on power spectrum amplitude are typically between 10^{-2} and 10^{-1}.

Constraints depend on the scale and parameterization of the curvature spectrum.

Growth of density perturbations prior to horizon entry affects the constraints.

Abstract

Primordial black holes (PBHs) can form in the early Universe via the collapse of large density perturbations. There are tight constraints on the abundance of PBHs formed due to their gravitational effects and the consequences of their evaporation. These abundance constraints can be used to constrain the primordial power spectrum, and hence models of inflation, on scales far smaller than those probed by cosmological observations. We compile, and where relevant update, the constraints on the abundance of PBHs before calculating the constraints on the curvature perturbation, taking into account the growth of density perturbations prior to horizon entry. We consider two simple parameterizations of the curvature perturbation spectrum on the scale of interest: constant and power-law. The constraints from PBHs on the amplitude of the power spectrum are typically in the range 10^{-2}-10^{-1} with some scale dependence.