Escher in the Sky

Renata Kallosh; Andrei Linde

doi:10.1016/j.crhy.2015.07.004

Escher in the Sky

Renata Kallosh ¹ ; Andrei Linde ¹

¹ Department of Physics and SITP, Stanford University, Stanford, CA 94305, USA

Comptes Rendus. Physique, Cosmic inflation / Inflation cosmique, Volume 16 (2015) no. 10, pp. 914-927.

Abstract
Résumé

We give a brief review of the history of inflationary theory and then concentrate on the recently discovered set of inflationary models called cosmological α-attractors. These models provide an excellent fit to the latest observational data. Their predictions $n_{s} \approx 1 - 2 / N$ and $r \approx 12 α / N^{2}$ are very robust with respect to the modifications of the inflaton potential. An intriguing interpretation of α-attractors is based on a geometric moduli space with a boundary: a Poincaré disk model of a hyperbolic geometry with the radius $\sqrt{3 α}$ , 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 Poincaré disk.

Après une brève revue de l'histoire de la théorie de l'inflation, cet article introduit une classe de modèles inflationaires récemment découverte : les << attracteurs de type α >>. Ces modèles offrent un très bon accord avec les données observationnelles. Leur prédiction sur l'indice spectral et le rapport tenseur–scalaire, $n_{s} \approx 1 - 2 / N$ et $r \approx 12 α / N^{2}$ , est très robuste vis-à-vis d'une modification du potentiel de l'inflaton. Une interprétation surprenante de ces attracteurs α repose sur la géométrie des espaces de modules avec bord : celle d'un disque hyperbolique de Poincaré de rayon $\sqrt{3 α}$ , merveilleusement représenté par le dessin Circle Limit IV d'Escher. Dans ces modèles, l'amplitude des ondes gravitationnelles est proportionnelle au carré du rayon du disque de Poincaré.

Published online: 2015-08-25

DOI: 10.1016/j.crhy.2015.07.004

Keywords: Inflation, Supergravity, Geometry
Mots-clés : Inflation, Supergravité, Géométrie

Author's affiliations:

Renata Kallosh ¹; Andrei Linde ¹

¹ Department of Physics and SITP, Stanford University, Stanford, CA 94305, USA

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Renata Kallosh; Andrei Linde. Escher in the Sky. Comptes Rendus. Physique, Cosmic inflation / Inflation cosmique, Volume 16 (2015) no. 10, pp. 914-927. doi : 10.1016/j.crhy.2015.07.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.07.004/

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