Fitting power spectrum of scalar perturbations for primordial black hole production during inflation

Abstract

We propose a simple analytic fit for the power spectrum of scalar (curvature) perturbations during inflation, in order to describe slow roll of inflaton and formation of primordial black holes in the early universe, in the framework of single-field models. Our fit is given by a sum of the power spectrum in the slow-roll approximation, needed for a viable description of the cosmic microwave background radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient production of primordial black holes. We use the T-type $\alpha$-attractor models in order to describe slow-roll inflation. Demanding the location and height of the peak to yield the masses of primordial black holes in the asteroid-size window allowed for the whole (current) dark matter to be composed of the primordial black holes, we find the restrictions on the remaining parameters and, most notably, on the width of the peak.

13 pages, 5 figures, LaTeX; Section 4 expanded, one figure and two references added

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Cited by in corpus (13)

• Quantum loop effects on the power spectrum and constraints on primordial black holes
• Galileon inflation evades the no-go for PBH formation in the single-field framework
• Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology
• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Large fluctuations and Primordial Black Holes
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• Are single-field models of inflation and PBHs production ruled out by ACT observations?
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Production of primordial black holes in improved E-models of inflation
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Improved model of large-field inflation with primordial black hole production in Starobinsky-like supergravity
• Single-field D-type inflation in the minimal supergravity in light of Planck-ACT-SPT data