A model describing an expanding universe containing matter and radiation, but without a cosmological constant. Such a universe is both homogeneous and isotropic. There is, in fact, a family of such universes including those which expand forever (open universe), those that eventually collapse (closed universe), and the particular example of the Einstein–de Sitter universe which has a critical density of matter. The geometry of spacetime in these universes is described by the Robertson–Walker metric and is, in the preceding examples, negatively curved, positively curved, and flat respectively (see curvature of spacetime). The Friedmann models, originated by the Russian mathematician Alexander Alexandrovich Friedmann (1888–1925), form the basis of the standard Big Bang theory.