# Constraints on the curvature power spectrum from primordial black hole evaporation

## TL;DR

This paper derives upper limits on the primordial curvature power spectrum based on the non-detection of sub-solar mass black holes, considering Hawking radiation effects and various early universe scenarios.

## Contribution

It provides new constraints on the amplitude of primordial perturbations across all scales, especially in the low mass PBH regime, accounting for different cosmic histories.

## Key findings

- Upper bounds on the variance of density perturbations for any reheating temperature.
- Constraints applicable to models generating low-mass primordial black holes.
- Implications for inflationary models producing PBHs.

## Abstract

We estimate the maximum allowed amplitude for the power spectrum of the primordial curvature perturbations, ${\cal P_R}(k)$, on all scales from the absence of any detection signals of sub-solar mass black holes. In particular we analyze the constraints on the PBHs and we focus on the low mass limit where the Hawking radiation is expected to significantly influence the big bang observables, considering also different early cosmic histories. We derive the upper bounds for the variance of density perturbations, $\sigma(M)$, for any possible reheating temperature as well as for the cosmological scenario of a scalar condensate domination. We expect our results to have considerable implications for models designed to generate PBHs, especially in the low mass range, and provide additional constraints to a large class of inflationary models.