Assumptions
The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the Cosmological Principle; empirically, this is justified on scales larger than ~100 Mpc. The Cosmological Principle implies that the metric of the universe must be of the form:
where is a three dimensional metric that must be one of (a) flat space, (b) a sphere of constant positive curvature or (c) a hyperbolic space with constant negative curvature. The parameter discussed below takes the value 0, 1, -1 in these three cases respectively. It is this fact that allows us to sensibly speak of a "scale factor", .
Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. The resulting equations are described below.
Read more about this topic: Friedmann Equations
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—George Bernard Shaw (1856–1950)