A Two - Point Correlation Function For The Universe, Gravity Into A Group

In the Universe, forced by gravitation matter tends to group together to form clusters. The detailed analysis of the galaxy and cluster distributions is usually given by the study of their statistical properties. The most important one is the two-point correlation function, which, in this paper, we mainly focus on. Our main work is as following: (1) By applying the max entropy method to the mean field theory of the correlation function, we get a formula for the two-point correlation function of galaxy distribution, which accords with the observed result. (2) Performing a scaling analysis to the Vlasov equations, which describes gravitational clustering, we derive a formula for the amplitude radio of galaxy and cluster correlations. Then, we obtain a probable relation between the cosmological scale factor and time. It is found that our conclusion agrees with the Q-field model of an accelerated expanding universe, and some parameters of the Q-field model are fixed.