“The Big Bang model of cosmology rests on two key ideas that date back to the early 20th century: General Relativity and the Cosmological Principle. By assuming that the matter in the universe is distributed uniformly on the largest scales, one can use General Relativity to compute the corresponding gravitational effects of that matter. Since gravity is a property of space-time in General Relativity, this is equivalent to computing the dynamics of space-time itself. The story unfolds as follows:

Possible space curvatures of the universe: Closed, Flat, Open. Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms, as shown schematically in the picture at left. It can be “positively” curved like the surface of a ball and finite in extent; it can be “negatively” curved like a saddle and infinite in extent; or it can be “flat” and infinite in extent – our “ordinary” conception of space. A key limitation of the picture shown here is that we can only portray the curvature of a 2-dimensional plane of an actual 3-dimensional space! Note that in a closed universe you could start a journey off in one direction and, if allowed enough time, ultimately return to your starting point; in an infinite universe, you would never return.”