J. F. Nicoll

Statistically efficient testing of the Hubble and Lundmark laws on IRAS galaxy samples

The local redshift-distance (z-r) power laws, z∞r p , of exponents p=1, 2, which are predicted respectively by generic big bang cosmology and chronometric cosmology, are tested on flux- and redshift-limited subsamples of the sample of Strauss et al. (1992). The completeness of this sample at 60 μm makes possible statistically optimal nonparametric estimates of the corresponding luminosity functions, which are used for the tests. The present analysis is basically free of assumptions regarding the spatial distribution of the galaxies; only the absence of selection on flux down to its limiting value, at each given redshift, is used

The nature of the redshift and directly observed quasar statistics.

The nature of the cosmic redshift is one of the most fundamental questions in modern science. Hubbles discovery of the apparent Expansion of the Universe is derived from observations on a small number of galaxies at very low redshifts. Today, quasar redshifts have a range more than 1000 times greater than those in Hubbles sample, and represent more than 100 times as many objects. A recent comprehensive compilation of published measurements provides the basis for a study indicating that quasar observations are not in good agreement with the original predictions of the Expanding Universe theory, but are well fit by the predictions of an alternative theory having fewer adjustable parameters.

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 the further assumption that the redshift is a Doppler effect, which is not made here. For each p, predictions of cosmology-independent quantities are derived from nonparametric maximum-likelihood estimates of the luminosity function, on the basis of the sample complete in angular diameter of de Vaucouleurs et al. (1991), consisting of more than 10,000 galaxies. These predictions are then compared with the directly observed values.

Astronomy phenomenological analysis of redshift-distance power laws

The traditional astronomical literature accepts the linear redshift-distance law on the basis of its internal consistency with accepted models of the history of the universe more than on nontrivial clearly objective tests of the linear law for directly observed quantities. The reluctance to depend on such tests rested historically on the assumed large variation in the intrinsic luminosity of extragalactic objects and a distrust of curve-fitting and statistics. But such tests are eminently feasible on the basis of modern objectively specified samples and up-to-date statistical methodology. This paper compares red-shift distance relations of the form z=k rp, for real values of p. Data from the visible, infrared, radio, and X-ray bands are examined. The deviation of predicted and observed apparent magnitudes, (a), and the difference between observed and predicated slope of the magnitude-log (z) plots,(b), are used to compare values of p. In summary, the p=1 values (corresponding to standard linear law) are more deviant than any other value of p, 1<p<=4for test (a) and more deviant than any value of p, 1<p<=3for test (b) except for marginal features in the smallest(radio) sample and in the lowest redshift sample. Bright subsamples and a morphologically homogeneous subsample of elliptic galaxies are also tested with similar results. In contrast, the predications for p=2 are reasonably accurate and close to optimal among all values of p explored. The p=2 case is predicted by the chronometric cosmology and in agreement with the independent analysis of Troitskii.