Higher-order m-theory corrections and the Kac-Moody algebra E10

It has been conjectured that the classical dynamics of M-theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E-10/K(E-10), where K(E-10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E-10. We here provide further evidence for this conjecture by showing that the leading higher-order corrections, quartic in the curvature and related 3-form-dependent terms, correspond to negative imaginary roots of E-10. The conjecture entails certain predictions for which higher-order corrections are allowed: in particular corrections of type R-M(DF)(N) are compatible with E-10 only for M+N = 3k+1. Furthermore, the leading parts of the R-4, R-7,.... terms are predicted to be associated with singlets under the sl(10) decomposition of E-10. Although singlets are extremely rare among the 4400 752 653 representations of sl(10) appearing in E-10 up to level l <= 28, there are indeed singlets at levels l = 10 and l = 20 which do match with the R-4 and the expected R-7 corrections. Our analysis indicates a far more complicated behaviour of the theory near the cosmological singularity than suggested by the standard homogeneous ansatze.