Statistical invalidation of the Hubble law.

An optimal nonparametric technique for elimination of the observation cutoff bias, on the assumption of a given theoretical cosmology, is applied to the redshift-magnitude and redshift-angular diameter relationships in objectively specified large galaxy samples. The estimates obtained on the assumptions of linear and square redshift-distance laws are uniformly and strongly favorable to the square law. The question of whether the relative inferiority of the linear law can scientifically be ascribed to ancillary extragalactic phenomena is addressed by nonparametric crosstesting of the alternative hypotheses. Each law is used to predict the results of a statistical analysis based on the alternative law by using the given data and computer simulations. The result is that the square law predicts with statistical exactitude the results of the analyses of the linear law; but the linear law predicts with near certainty that the fit of the square law will be much worse than is observed. In the absence of independent validation of a variety of ancillary hypotheses that have been adduced in connection with the linear law, it seems necessary to conclude that the Hubble law lacks an objective statistical foundation.