Primordial Black Holes from $\alpha$-attractors

Abstract

We consider primordial black hole (PBH) production in inflationary $\alpha$-attractors. We discuss two classes of models, namely models with a minimal polynomial superpotential as well as modulated chaotic ones that admit PBHs. We find that a significant amplification of the curvature power spectrum ${\mathcal{P}}_{\mathcal{R}}$ can be realized in this class of models with a moderate tuning of the potential parameters. We consistently examine the PBH formation during radiation and additionally during reheating eras where the background pressure is negligible. It is shown that basic features of the curvature power spectrum are explicitly related with the postinflationary cosmic evolution and that the PBH mass and abundance expressions are accordingly modified. PBHs in the mass range $10^{-16}-10^{-14}{M}_{\odot }$ can form with a cosmologically relevant abundance for a power spectrum peak ${\mathcal{P}}_{\mathcal{R}}\sim 10^{-2}$ and large reheating temperature and, furthermore, for a moderate peak ${\mathcal{P}}_{\mathcal{R}}\sim 10^{-5}$ and reheating temperature $T_{\text{rh}}\sim 10^7$ GeV, characteristic of the position of the power spectrum peak. Regarding the CMB observables, the $\alpha$-attractor models utilized here to generate PBH in the low-mass region predict in general a smaller $n_s$ and larger $r$ and ${\alpha }_s$ parameter values compared to the conventional inflationary $\alpha$-attractor models.

34 pages, 12 figures with 33 plots. Minor corrections. References added. In this version there are updated parameters for our inflationary models in accordance with the Planck 2018 results. Journal version

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