Primordial black hole formation in inflationary $\alpha$-attractor models

TL;DR

This paper investigates primordial black hole formation within superconformal inflationary $ ext{alpha}$-attractor models, demonstrating how specific potential tuning can produce PBHs in the $10^{16}$ to $10^{18}$ gram range and associated gravitational waves.

Contribution

It introduces a fine-tuned inflaton potential in $ ext{alpha}$-attractors that generates primordial black holes and calculates the resulting gravitational wave spectrum.

Findings

Primordial black holes in the mass range $10^{16}$ to $10^{18}$ g can be produced.

The model predicts a peak in curvature perturbation at $ ext{~}10^{14} ext{ Mpc}^{-1}$.

Second order gravitational wave spectrum is computed based on the curvature enhancement.

Abstract

The formation of primordial black holes is studied using superconformal inflationary $\alpha$-attractors. An inflaton potential is constructed with a plateau-like region which brings about the onset of an ultra slow-roll region where the required enhancement in the curvature power spectrum takes place. This is accomplished by carefully fine-tuning the parameters in the potential. For the parameter sets, the amount of observable inflation is such that the curvature perturbation $\mathcal{P}_{\mathcal{R}}$ peaks at $\sim 10^{14}\text{Mpc}^{-1}$, producing PBHs in the mass window $10^{16}\text{g}\leq M \leq 10^{18}\text{g}$. The reheating period after inflation is taken into account to determine whether or not PBH formation takes place in such a phase. Finally, the spectrum of second order gravitational waves, that can arise due to the curvature perturbation enhancement, is calculated.