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Large Field Inflation and Double $α$-Attractors

We consider a broad class of inflationary models that arise naturally in supergravity. They are defined in terms of a parameter $α$ that determines the curvature and cutoff of these models. As a function of this parameter, we exhibit that the inflationary predictions generically interpolate between two attractor points. At small cutoff $α$, the resulting inflationary model is of plateau-type with $n_s = 1 - 2 / N$ and $r = 12 α/ N^2$. For $α= 1$, these predictions coincide with predictions of the Starobinsky model and Higgs inflation. In contrast, for large cutoff $α$, the theory asymptotes to quadratic inflation, with $n_s = 1 - 2 / N$, $r = 8 / N$. Both universal predictions can be attributed to a stretching of the moduli space. For intermediate values of $α$, the predictions interpolate between these two critical points, thus covering the sweet spots of both Planck and BICEP2.