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 $E_{10}/K(E_{10})$, where $K(E_{10})$ is the maximal compact subgroup of the hyperbolic Kac-Moody group $E_{10}(\mathbb{R})$. For the proof we make use of a novel decomposition of $E_{10}$ into irreducible representations of its $\mathrm{S}\mathrm{L}(10,\mathbb{R})$ subgroup. We explicitly show how to identify the first four rungs of the $E_{10}$ coset fields with the values of geometric quantities constructed from $D=11$ supergravity fields and their spatial gradients taken at some comoving spatial point.

• Received 31 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.221601