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

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 $10^{16}\text{g}\le M\le 10^{18}\text{g}$. 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.

29 pages, 10 figures, corrected typos, updated final section and references

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