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

TL;DR

This paper investigates primordial black hole formation within $ ext{alpha}$-attractor inflation models using optimized peaks theory, revealing larger predicted PBH masses and implications for future gravitational wave constraints.

Contribution

It introduces the application of optimized peaks theory to $ ext{alpha}$-attractor models, showing larger PBH masses and shifted power spectrum peaks compared to traditional methods.

Findings

Horizon mass of PBHs is larger by about an order of magnitude.

PBHs can form from lower peak values of the curvature power spectrum.

Predicted PBH masses are larger, affecting future observational constraints.

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 r\^{o}le 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.