Primordial black hole formation in $\alpha$-attractor models: an analysis using optimized peaks theory

Abstract

In this paper, the formation of primordial black holes (PBHs) is reinvestigated using inflationary $\alpha$-attractors. Instead of using the conventional Press-Schechter theory to compute the abundance, the optimized peaks theory is used, which was developed in Ref. \cite{Yoo:2018kvb,Yoo:2020dkz}. This method takes into account how curvature perturbations play a rôle in modifying the mass of primordial black holes. Analyzing the model proposed in \cite{Mahbub:2019uhl} it is seen that the horizon mass of the collapsed Hubble patch is larger by $\mathcal{O}(10)$ compared to the usual computation. Moreover, PBHs can be formed from curvature power spectrum, ${\mathcal{P}}_{\zeta }(k)$, peaked at lower values using numerically favored threshold overdensities. As a result of the generally larger masses predicted, the peak of the power spectrum can be placed at larger $k$ modes than that is typical with which potential future constraints on the primordial power spectrum through gravitational waves (GWs) can be evaded.

arXiv comment13 pages, 8 captioned figures; some computational errors have been corrected, leading to different results compared to the version 1 preprint; accepted for publication in PRD

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