Why is the Universe Isotropic?

We examine the question of whether the present isotropic state of the universe could have resulted from initial conditions which were "chaotic," in the sense of being arbitrary, any anisotropy dying away as the universe expanded. We show that the set of spatially homogeneous cosmological models which approach isotropy at infinite times is of measure zero in the space of all spatially homogeneous models. This indicates that the isotropy of the Robertson-Walker models is unstable to homogeneous and anisotropic perturbations. It therefore seems that there is only a small set of initial conditions that would give rise to universe models which would be isotropic to within the observed limits at the present time. One possible way out of this difficulty is to suppose that there is an infinite number of universes with all possible different initial conditions. Only those universes which are expanding just fast enough to avoid recollapsing would contain galaxies, and hence intelligent life. However, it seems that this subclass of universes which have just the escape velocity would in general approach isotropy. On this view, the fact that we observe the universe to be isotropic would be simply a reflection of our own existence. Subject headings: cosmic background radiation - cosmology - relativity