Constraints from primordial black hole formation at the end of inflation

TL;DR

This paper investigates how primordial black hole constraints limit inflation models, especially those with large small-scale perturbations, by using a modified analysis and numerical evolution to exclude models that overproduce PBHs.

Contribution

It introduces a modified flow analysis and numerical methods to accurately evaluate small-scale perturbations and constrain inflation models based on PBH overproduction.

Findings

PBH constraints exclude certain inflation models with large small-scale perturbations.

Numerical evaluation reduces the number of viable inflation models.

Models with indefinite inflation ending via secondary mechanisms are significantly constrained.

Abstract

Primordial black hole (PBH) abundance limits constrain the primordial power spectrum, and hence models of inflation, on scales far smaller than those probed by cosmological observations. Single field inflation models which are compatible with all cosmological data can have large enough perturbations on small scales to overproduce PBHs, and hence be excluded. The standard formulae for the amplitude of perturbations do not hold for modes that exit the horizon close to the end of inflation however. We use a modified flow analysis to identify models of inflation where the amplitude of perturbations on small scales is large. For these models we then carry out a numerical evolution of the perturbations and use the PBH constraints on the power spectrum to eliminate models which overproduce PBHs. Significant PBH formation can occur in models in which inflation can continue indefinitely and is ended via a secondary mechanism. We demonstrate that PBHs constrain these types of inflation models and show that a numerical evaluation of the power spectrum decreases the number of otherwise viable models of inflation.