Primordial black holes through preheating instabilities in $\alpha$-attractor models

TL;DR

This paper investigates primordial black hole formation during the preheating phase of $ ext{α}$-attractor inflation models, emphasizing the importance of nonspherical effects and collapse criteria for accurate abundance predictions.

Contribution

It introduces a detailed analysis of PBH formation criteria during preheating and compares Press-Schechter and Khlopov-Polnarev formalisms, highlighting the significance of nonspherical effects.

Findings

Press-Schechter overestimates PBH abundance during preheating.

Khlopov-Polnarev formalism provides more realistic PBH predictions.

Observational constraints exclude PS-based PBH predictions, KP remains viable.

Abstract

In this work, we explore the production of primordial black holes (PBHs) within the context of $\alpha$-attractor inflationary models, focusing on the preheating phase following inflation. During this phase, self-resonance instabilities arise due to deviations of the inflationary potential from a quadratic form. PBH formation is analyzed using three criteria: (1) the perturbation must lie within the instability band, (2) its characteristic length must exceed the Jeans length, and (3) it must have sufficient time to collapse based on the estimations of massive scalar field spherical collapse in Einstein-de Sitter universe. Based on these criteria, we calculate the PBH mass fraction using the Press-Schechter (PS) and Khlopov-Polnarev (KP) formalisms. Our results show that the PS formalism tends to overestimate PBH abundance during preheating, as it neglects nonspherical effects. In contrast, the KP formalism yields more realistic predictions by incorporating such effects. We provide a detailed comparison with observational constraints from evaporating PBHs. Notably, the PS formalism is excluded by these constraints, which are based on Hawking radiation, while the KP formalism remains viable. These findings underscore the importance of accounting for nonspherical effects and accurate collapse dynamics in studies of PBH formation during preheating.