Superconformal Inflationary $\alpha$-Attractors

Abstract

Recently a broad class of superconformal inflationary models was found leading to a universal observational prediction $n_s=1-2/N$ and $r=12/N^2$. Here we generalize this class of models by introducing a parameter $\alpha$ inversely proportional to the curvature of the inflaton Kahler manifold. In the small curvature (large $\alpha$) limit, the observational predictions of this class of models coincide with the predictions of generic chaotic inflation models. However, for sufficiently large curvature (small $\alpha$), the predictions converge to the universal attractor regime with $n_s=1-2/N$ and $r=12\alpha/N^2$, which corresponds to the part of the $n_s-r$ plane favored by the Planck data.