E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology

2000/12/31 by Thibault Damour, Marc Henneaux · 9 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #astro-ph #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevlett.86.4749

published as Phys.Rev.Lett.86:4749-4752,2001 · 4 pages, 1 figure, minor changes in the text, two references added

arxiv created 2001/04/12 · openalex publication_date 2001/05/21 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

It is shown that the never ending oscillatory behaviour of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in 9-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E₁₀ (for type II) or BE₁₀ (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic (``Anosov'') nature of the classical cosmological oscillations, and suggest a ``chaotic quantum billiard'' scenario of vacuum selection in string theory.

Cited by

• The pre-big bang scenario in string cosmology
• Describing general cosmological singularities in Iwasawa variables
• Nonlinear bigravity and cosmic acceleration
• The Weyl tensor in spatially homogeneous cosmological models
• Cosmological backgrounds of superstring theory and solvable algebras: oxidation and branes
• Supersymmetric quantum cosmological billiards
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• The topology of U-duality (sub)groups
• Marc Henneaux [wikipedia]