Inflationary $\alpha$-attractors from $F(R)$ Gravity

TL;DR

This paper explores the connection between $eta$-attractor inflation models and $F(R)$ gravity, showing that the attractor behavior persists in the $F(R)$ framework and deriving approximate forms of these models.

Contribution

It establishes the equivalence of $eta$-attractor models in $F(R)$ gravity and derives their approximate forms, extending the attractor paradigm.

Findings

Spectral index and scalar-to-tensor ratio match $R^2$ model predictions.

Attractor property persists in $F(R)$ gravity for $eta$-attractors.

Implicit and approximate forms of $F(R)$ inflationary models are obtained.

Abstract

In this paper we study some classes of $\alpha$-attractors models in the Jordan frame and we find the corresponding $F(R)$ gravity theory. We study analytically the problem at leading order and we investigate whether the attractor picture persists in the $F(R)$ gravity equivalent theory. As we show, if the slow-roll conditions are assumed in the Jordan frame, the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio are identical to the corresponding observational indices of the $R^2$ model, a result which indicates that the attractor property is also found in the corresponding $F(R)$ gravity theories of the $\alpha$-attractors models. Moreover, implicit and approximate forms of the $F(R)$ gravity inflationary attractors are found.