The expansion of the Universe

It is shown that, in principle, the observed galactic redshifts and microwave background radiation in the Universe can be explained by a static spherically symmetric (or SSS) universe model, in which there is a singularity which continually interacts with the Universe. However, when Einstein's field equations are introduced with a plausible equation of state, a good fit cannot be obtained to the observed (m,z) relation in a SSS universe model with all the properties required. The standard discussions of the expansion of the Universe proceed from an unverified a priori assumption - the Cosmological Principle - and deduce that the Universe is expanding, on the basis of that assumption. The present result constitutes a proof that the Universe is expanding, which is not based on a priori assumptions about space-time geometry. Such a proof is needed if one is seriously to attempt to make cosmology an observationally-based subject. In addition, the SSS models are used to point out various features of interest that could arise in expanding, inhomogeneous universe models. Particularly, it is shown that an observer cannot deduce from the isotropy of the microwave background radiation, that the Universe is spherically symmetric about him; and that there may exist plausible cosmological models with a 'continuously active' singularity, such as is envisaged for the SSS universe models. (author)