Considerations of the shape of the universe can be split into two parts; the local geometry relates especially to the curvature of the observable universe, while the global geometry relates especially to the topology of the universe as a whole—which may or may not be within our ability to measure.<br /><br />The extrapolation of the local geometry of space to the geometry of the whole universe is not without a specific ontological stance regarding how space and time coexist. Current thinking demands that space and time be considered as two aspects of a single 'spacetime'.<br /><br />Nevertheless it still makes sense to speak about three-dimensional concepts referring to the universe, like the Hubble volume.<br /><br /><br />[edit] Local geometry (spatial curvature)<br />The local geometry is the curvature describing any arbitrary point in the observable universe (averaged on a sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation, show the observable universe to be very close to homogeneous and isotropic and infer it to be accelerating. In General Relativity, this is modelled by the Friedmann-Lemaître-Robertson-Walker (FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature (often referred to as geometry) of the universe based on the mathematics of fluid dynamics, i.e. it models the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe.<br /><br />Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by th