Chaos and Symmetry in String Cosmology

We review the recently discovered interplay between chaos and symmetry in the general inhomogeneous solution of many string-related Einstein-matter systems in the vicinity of a cosmological singularity. The Belinsky-Khalatnikov-Lifshitz-type chaotic behaviour is found, for many Einstein-matter models (notably those related to the low-energy limit of superstring theory andM-theory), to be connected with certain (infinite-dimensional) hyperbolic KacMoody algebras. In particular, the billiard chambers describing the asymptotic cosmological behaviour of pure Einstein gravity in spacetime dimension d + 1, or the metric-three-form system of 11dimensional supergravity, are found to be identical to the Weyl chambers of the Lorentzian Kac-Moody algebras AEd, or E10, respectively. This suggests that these Kac-Moody algebras are hidden symmetries of the corresponding models. There even exists some evidence of a hidden equivalence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E10/K(E10), where K(E10) is the maximal compact subgroup of E10. Invited talk at the 11th Marcel Grossmann Meeting on Recent Developments in General Relativity, Berlin, Germany, 23-29 July 2006.