One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production

TL;DR

This paper calculates one-loop quantum corrections to inflationary models predicting primordial black holes, showing they are small but relevant for dark matter and gravitational wave signals, with potential for future detection.

Contribution

It provides a numerical analysis of one-loop corrections in E-type α-attractor inflation models and explores their implications for primordial black hole formation and gravitational wave signals.

Findings

One-loop corrections contribute only a few percent to the power spectrum.

Models can produce asteroid-mass PBHs consistent with CMB and distortion constraints.

PBHs could constitute a significant fraction of dark matter and generate detectable gravitational waves.

Abstract

The one-loop corrections (1LC) to the power spectrum of scalar perturbations arising from cubic interactions in the single-field E-type $\alpha$-attractor models of inflation and primordial black hole (PBH) production are numerically calculated. The results demonstrate the 1LC contributes merely a few percent to the tree-level power spectrum. The model parameters are chosen to predict the PBH masses in the asteroid-mass range, while maintaining consistency with the cosmic microwave background (CMB) observations within 1$\sigma$ confidence levels, and obeying the upper limits on $\mu$-distortions. The PBHs formed on scales smaller than the inflation scale can constitute a significant fraction of the present dark matter (DM). The PBH-induced gravitational waves (GW) may be detectable by the future space-based gravitational interferometers. We also consider a reconstruction of the scalar potential from possible GW observations and present a numerical approach tested in the model parameter space.