Primordial blackhole formation: Exploring chaotic potential with a sharp step via the GLMS perspective

TL;DR

This paper investigates how a sharp step in a chaotic inflationary potential can lead to primordial black hole formation across multiple mass ranges, using the GLMS peak theory approximation and comparing it with the Press-Schechter formalism, aligning with observational constraints.

Contribution

It introduces a model with a sharp step in the potential that produces PBHs in four mass ranges and compares two different methods for calculating their abundance.

Findings

GLMS approximation predicts near-unity PBH abundance in small mass windows.

Press-Schechter formalism yields significantly lower PBH abundance.

Results are consistent with current observational constraints.

Abstract

A sharp step on a chaotic potential can enhance primordial curvature fluctuations on smaller scales to the $\mathcal{O}(10^{-2})$ to form primordial black holes (PBHs). The present study discusses an inflationary potential with a sharp step that results in the formation of PBHs in four distinct mass ranges. Also this inflationary model allows the separate consideration of observable parameters $n_s$ and $r$ on the CMB scale from the physics at small scales, where PBHs formation occur. In this work we computed the fractional abundance of PBHs ($f_{PBH}$) using the GLMS approximation of peak theory and also the Press-Schechter (PS) formalism. In the two typical mass windows, $10^{-13}M_\odot$ and $10^{-11}M_\odot$, $f_{PBH}$ calculated using the GLMS approximation is nearly equal to 1 and that calculated via PS is of $10^{-3}$. In the other two mass windows $1M_\odot$ and $6M_\odot$, $f_{PBH}$ obtained using GLMS approximation is 0.01 and 0.001 respectively, while $f_{PBH}$ calculated via PS formalism yields $10^{-5}$ and $10^{-6}$. The results obtained via GLMS approximation are found to be consistent with observational constraints. A comparative analysis of $f_{PBH}$ obtained using the GLMS perspective and the PS formalism is also included.