E10, BE10 and arithmetical chaos in superstring cosmology.
It is shown that the neverending oscillatory behavior 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 nine-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.
Damour
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Institut des Hautes Etudes Scientifiques, 35, route de Chartres, F-91440 Bures-sur-Yvette, France.
Henneaux
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