New and Old Tests of Cosmological Models and the Evolution of Galaxies

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Abstract
We describe classical cosmological tests, such as the log N-log S, redshift-magnitude, and angular diameter tests, and propose some new tests of the evolution of galaxies and the universe. Most analyses of these tests treat the problem in terms of a luminosity function and its evolution. The main thrust of this paper is to show that this is inadequate and can lead to incorrect conclusions when dealing with high-redshift sources. We develop a proper treatment in three parts. First, we describe these tests based on the isophotal values of quantities such as flux, size, or surface brightness. We show the shortcomings of the simple point-source approximation based solely on the luminosity function and consideration of the flux limit. We emphasize the multivariate nature of the problem and quantify the effects of other selection biases arising from the surface brightness and angular size limitations. In these considerations, the surface brightness profile and the distribution of the basic parameters describing it play a critical role in modeling the problem. In general, in the isophotal scheme the data analysis and comparison with the model predictions is complicated. Next, we show that considerable simplification is achieved if these test are carried out in some sort of metric scheme, for example that suggested by Petrosian. This scheme, however, is limited to well-resolved sources. Finally, we describe the new tests and compare them to the traditional tests, demonstrating the observational and modeling ease that they provide. These new procedures, which can use the data to a fuller extent than the isophotal or metric-based tests, amount to simply counting the pixels or adding their intensities as a function of the surface brightness of all galaxies instead of dealing with surface brightness, size, and flux (or magnitude) of individual galaxies. We also show that a comparison of the data with the theoretical models of the distributions and evolution of galaxies has the simplicity of the metric test and utilizes the data as fully as the isophotal test.
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