Generalized non-minimal derivative coupling: application to inflation and primordial black hole production

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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.