Geometry of the expanding Universe

Definitive conclusions may be drawn occasionally even from incomplete information. Indeed, employing a remarkable interplay between various areas of modern mathematics, one is able to discuss the entire class of spacetime geometries that may serve as backgrounds for the consistent propagation of matter. Such generalized geometries emerge from theories of quantum gravity, but also provide a far-reaching geometric point of view to the spectacular experimental observation that our universe expands at an accelerated rate.