A Mathematical Framework for Discussing the Statistical Distribution of Galaxies in Space and its Cosmological Implications

Citation

Gunn, James Edward (1966) A Mathematical Framework for Discussing the Statistical Distribution of Galaxies in Space and its Cosmological Implications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EV32-TQ73. https://resolver.caltech.edu/CaltechETD:etd-11052003-090546

Abstract

The spectral-theoretic techniques of stationary time-series analysis are generalized and applied to the study of the statistical distribution of galaxies in space and the observed distribution on the sky. Sampling techniques and criteria are developed for the measurement of the Fourier transform of the autocovariance function, the so-called "power spectrum". The theory is extended to curved, nonstatic space-times and the possibility of using the spectral density obtained from counts of galaxies in the formulation of cosmological tests is discussed. A similar development is made for the statistical structure of the background light due to very faint galaxies, and the possibility of measurement of this structure and its application to cosmological tests is considered. It is shown that in both cases (counts and background) significant cosmological data can be obtained if our knowledge of the luminosity function, the spectra, and the evolution of galaxies is improved. Finally, application is made of the theory to the analysis of a small count problem in order to learn something about the general form of the spatial covariance.

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