Cosmological Matter Density Fluctuation Field Theory

By studying the mass density distribution of the Newtonian self-gravitating system, we can estimate the mass density distribution in the Universe i.e. the galaxy-galaxy or cluster-cluster correlation function ξ(r). Modeling the system either as a gas in thermal equilibrium, or as a fluid in hydrostatical equilibrium, we obtain the field equation of correlation function ξ(r) of the mass density fluc-tuation itself and compare the solution with the observational data.The equation tells that ξ(r) depends on the point mass m and Jeans wave-length scale λ0, which are different for galaxies and clusters. It explains several prominent features of the observed clustering:the profile of ξcc(r) of clusters is similar to ξgg(r) of galaxies but with a higher amplitude and a longer correlation length, the correlation length increases with the mean separation between clusters τ0(?)0.4d as the observed scaling, and on very large scalesξcc(r) exhibits periodic oscillations with a characteristic wavelength-120Mpc. We take perturbation method and solve the equation to (δψ)2 order and (δψ)3 order respectively. With a set of fixed model parameters for each perturbation, the solution ξ(r) for galaxies and for clusters, the power spectrum, the projected, and the angular correlation function, simultaneously agree with the observational data from the surveys, such as Automatic Plate Measuring (APM), Two-degree-Field Galaxy Redshift Survey (2dFGRS), and Sloan Digital Sky Survey (SDSS). The higher order perturba-tion gives a better fit for the data, and the formulation may be considered as a theoretical method to study the clustering of matter in the Universe.