Inflationary α -attractors from F ( R ) gravity

In this paper, we study some classes of α-attractor 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 R2 model, a result which indicates that the attractor property is also found in the corresponding F(R) gravity theories of the α-attractor models. Moreover, implicit and approximate forms of the F(R) gravity inflationary attractors are found.