Generalized Non-Minimal Derivative Coupling: Application to Inflation and Primordial Black Hole Production

TL;DR

This paper introduces a new inflationary model with a field-dependent non-minimal derivative coupling to the Einstein tensor, called GNMDC, which offers novel predictions and can enhance primordial black hole production.

Contribution

It proposes the GNMDC framework within Horndeski theories, demonstrating its ability to address gradient instabilities and amplify small-scale perturbations for PBH formation, including using the Higgs potential.

Findings

GNMDC provides distinguishable inflationary predictions.

The model can amplify small-scale power spectrum for PBH production.

Inflation and PBH formation can be achieved with the Higgs potential.

Abstract

We introduce inflationary models where the inflaton features a field dependent non-minimal derivative coupling to the Einstein tensor, that we name GNMDC. This Horndeski term gives new and distinguishable inflationary predictions in a framework that ameliorates possible problems related with gradient instabilities during the reheating stage. We examine the inflationary phenomenology using power law monomial and exponential potentials. We further elaborate on the implications of the inflaton-modulated GNMDC and construct GNMDC terms that can amplify the power spectrum of primordial perturbations at small scales, triggering PBH production. An attractive feature of the GNMDC is that inflation, as well as PBH production, can be implemented utilizing the Higgs potential.