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

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.

arXiv comment18 pages, 6 figures, LaTeX; references added

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• Inflation in $F(R)$ gravity models revisited after ACT
• Are single-field models of inflation and PBHs production ruled out by ACT observations?
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop