Seminar

Astronomical observations have long been interpreted to support a so-called 'cosmological principle' according to which the universe, viewed on a sufficiently large, coarse-grained scale, is spatially homogeneous and isotropic. Up to an overall, time-dependent scale factor, only three Riemannian manifolds are compatible with this principle, namely the constant curvature spaces S³, E³ and H³ or spherical, flat and hyperbolic space-forms respectively and these provide the bases for the standard Friedmann, Robertson-Walker, Lemaîtra (FRWL) cosmological models. But astronomers only observe a fraction of the universe and the possibility remains open that its actual topology could be more 'exotic' and perhaps only locally compatible with isotropy and homogeniety. In this talk I shall discuss some mathematical evidence suggesting that the Einstein field equations, formulated on much more general manifolds than the FRWL ones listed above, contain a dynamical mechanism according to which the universe will, in the direction of cosmological expansion, be volume dominated by regions that are asymptotically homogeneous and isotropic.