Hyperbolic geometry of cosmological attractors

By J. J. Carrasco, R. Kallosh, Andrei Linde, D. Roest. 2015

167 citations recorded by the source corpus.

Cosmological alpha attractors give a natural explanation for the spectral index n(s) of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincare disk or half plane in the supergravity construction. These geometries are isometric under Mobius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kahler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield alpha attractors.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/76ef7ccab83d469c79fd3eef11361a4732907230

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Citations in the corpus

α-attractors: Planck, LHC and dark energy (2015, methodology): “Another, also geometric, interpretation of this parameter is in terms of the Poincaré disk model of a hyperbolic geometry with the radius √ 3α, illustrated by the Escher’s picture Circle Limit IV [14, 15].”
Dark energy, α-attractors, and large-scale structure surveys (2017, methodology): “This employs the Kähler frame that has a manifest inflaton shift symmetry [105].”
Cosmological attractors and initial conditions for inflation (2015, methodology): “Indeed, as explained in [17], the Kähler potential (2.”