Spatial and Angular Correlation Functions in Cosmology

[摘要] The purpose of this thesis is to study the role of the spatial and angular correlation functions for galaxies and clusters of galaxies. We discuss the various approaches to the problem of describing the statistical distribution of galaxies and discuss the connection between Peebles' and Limber's approach. The former describes the distribution as a point process, the latter considers the density distribution as a random function or process. The density distribution that corresponds to a particular spatial correlation function can be generated by use of spectral analysis. We discuss some of the problems involved in generating the density distribution in this way, and use this description to derive the relationship between the angular and the spatial correlation function for particular forms of the latter. Selection effects are introduced first by simply truncating all galaxies beyond a certain distance, and secondly by introducing the Schechter luminosity function and excluding galaxies whose apparent magnitude is above some threshold value. We briefly review the fractal description of galaxy distributions, and relate this to the description in terms of spatial correlation functions.

[发布机构] University:University of Glasgow

[关键词] Astrophysics, Theoretical physics, Statistical physics