Escher in the Sky

Abstract

The cosmological models called $\hat{I}\pm$-attractors provide an excellent fit to the latest observational data. Their predictions $n_s=1-2/N$ and $r=12\hat{I}\pm /N^2$ are very robust with respect to the modifications of the inflaton potential. An intriguing interpretation of $\hat{I}\pm$-attractors is based on a geometric moduli space with a boundary: a Poincare disk model of a hyperbolic geometry with the radius $\sqrt{3\hat{I}\pm }$, beautifully represented by the Escher's picture Circle Limit IV. In such models, the amplitude of the gravitational waves is proportional to the square of the radius of the Poincare disk.

11 pages, 12 figures, Introductory part is extended, references added