FLRW cosmological models are those universes which are everywhere isotropic about the fundamental velocity (technically: there is a G3 group of isotropies acting about every spacetime point which leaves the fundamental velocity invariant). This will be the case if and only if the observations of every fundamental observer are isotropic at all times. This implies further symmetries of these universes: as well as being isotropic about each event, they are spatially homogeneous: all physical properties are the same everywhere on spacelike surfaces orthogonal to the fluid flow (technically: there is a G3 group of isometries acting simply transitively on these surfaces). This will be proved in the sequel, but geometrically the result is clear: spheres of constant density centred on one point P are only consistent with spheres of constant density centred on other points Q and R if the density is constant.

Because of these exact symmetries, these spacetimes cannot themselves be realistic models of the observed universe: they do not represent any of the inhomogeneities associated with the astronomical structures we see all around us. Realistic models of the observed universe are provided by perturbed FLRW universes, which are almost isotropic about every point, and hence are almost spatially homogeneous (they are inhomogeneous on small scales but homogeneous on large scales). The ‘almost FLRW’ models are the standard models of cosmology at the present time (considered in the following chapter).