REDSHIFT-MAGNITUDE RELATION IN HIERARCHICAL COSMOLOGIES

The usual redshift–magnitude relation is valid when the expansion rate of the Universe, though time-dependent, is uniform. Modifications due to larger-scale clustering are suggested. They are based on a model of light propagation in which light moves at a constant velocity with respect to the mean motion of the matter through which it passes. Specific results are obtained which could serve as a potential test of big-bang hierarchical cosmological models. In such models, there is in general a scale-dependence of the Hubble parameter. The main effect of this scale dependence would be to make current estimates of the deceleration parameter larger than the true values. Thus, present observational data could be made consistent with small or negative values of the true deceleration parameter, q 0—and, in particular, with the value q 0 = –1 associated with the steady-state model. © 1971 Royal Astronomical Society.