The metric can be written as:

where

These three possibilities correspond to parameter of (0) flat space, (+1) a sphere of constant positive curvature or (-1) a hyperbolic space with constant negative curvature.Here the radial position has been decomposed into a time-dependent scale factor, , and a comoving coordinate, . Inserting this metric into Einstein's field equations relate the evolution of this scale factor to the pressure and energy of the matter in the universe. With the stress-energy tensor

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