E₁₀ and a Small Tension Expansion of M Theory

A formal “small tension” expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite-dimensional coset space E₁₀/K(E₁₀), where K(E₁₀) is the maximal compact subgroup of the hyperbolic Kac-Moody group E₁₀(R). For the proof we make use of a novel decomposition of E₁₀ into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E₁₀ coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.