Inflationary<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-attractors from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

In this paper, we study some classes of $\ensuremath{\alpha}$-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 ${R}^{2}$ model, a result which indicates that the attractor property is also found in the corresponding $F(R)$ gravity theories of the $\ensuremath{\alpha}$-attractor models. Moreover, implicit and approximate forms of the $F(R)$ gravity inflationary attractors are found.

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