Generalized Rp-attractor cosmology in the Jordan and Einstein frames: New type of attractors and revisiting standard Jordan frame Rp inflation

Abstract

In this work, we study a new class of attractor models which we shall call generalized [Formula: see text]-attractor models. This class of models is based on a generalization of the Einstein frame potential of [Formula: see text] [Formula: see text] gravity models in the Jordan frame. We present the attractor properties of the corresponding nonminimally coupled Jordan frame theory, and we calculate the observational indices of inflation in the Einstein frame. As we show, there is a large class of nonminimally coupled scalar theories, with an arbitrary nonminimal coupling which satisfies certain conditions, that yield the same Einstein frame potential, this is why these models are characterized attractors. As we demonstrate, the generalized [Formula: see text]-attractor models are viable and well fitted within the Planck constraints. This includes the subclass of the generalized [Formula: see text]-attractor models, namely the Einstein frame potential of [Formula: see text] inflation in the Jordan frame, a feature also known in the literature. We also highlight an important issue related to the [Formula: see text] inflation in the Jordan frame, which is known to be nonviable. By conformal invariance, the [Formula: see text] inflation model should also be viable in the Jordan frame, which is not. We pinpoint the source of the problem using two different approaches in the [Formula: see text] gravity Jordan frame, and as we demonstrate, the problem arises in the literature due to some standard simplifications made for the sake of analyticity. We demonstrate the correct way to analyze [Formula: see text] inflation in the Jordan frame, using solely the slow-roll conditions.