PHENOMENOLOGY OF THE LOCAL ANGULAR DIAMETER TO REDSHIFT RELATION

A phenomenological study from first principles is made of the putative parameter p such that the redshift varies locally as the pth power of the distance. The Copernican principle implies that p = 1 only with t he further assumption that the redshift is a Doppler effect, which is not made here. For each p, predictions of cosmology-independent quanti ties are derived from nonparametric maximum-likelihood estimates of th e luminosity function, on the basis of the sample complete in angular diameter of de Vaucouleurs et al. (1991), consisting of more than 10,0 00 galaxies. These predictions are then compared with the directly obs erved values.