Large Field Inflation and Double $\alpha$-Attractors

Abstract

We consider a broad class of inflationary models that arise naturally in supergravity. They are defined in terms of a parameter $\alpha$ 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 $\alpha$, the resulting inflationary model is of plateau-type with $n_s=1-2/N$ and $r=12\alpha /N^2$. For $\alpha =1$, these predictions coincide with predictions of the Starobinsky model and Higgs inflation. In contrast, for large cutoff $\alpha$, 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 $\alpha$, the predictions interpolate between these two critical points, thus covering the sweet spots of both Planck and BICEP2.

Comments: 22 pages, 5 figures; v2: ref added