Shape of the Universe

Scientific models of the Universe are intended to satisfy the Einstein field equations, that roughly speaking, state that curvature = density and that mass density curves space. The models allow many different sorts of spaces, which have the local property called a metric (a sort of rule for locally measuring distances, that determines curvature) and have global properties that define them, such as topology. Together curvature and topology can be described as shape. The metric of the standard Universe model has many parameters such as the Hubble parameter, the baryon density parameter, the baryonic and non-baryonic dark matter density parameter Ωm, and the dark energy parameter ΩΛ. This standard model is oversimplified: it assumes that for the chosen separation of spacetime into space and time coordinates, the Universe is the same everywhere (homogeneous) in space at a given time coordinate.