Formation of difference in distribution between visible and invisible matters in the expanding universe

Abstract

The visible and invisible matters in the universe have rather different density distributions. The formar is obvious clustered on the scales of galaxies, clusters and superclusters, while the latter is rather more uniform. Here we discuss the possibility of this difference forming during the stage of Jeans clustering. For a two-component universe, so long as the growth and decay time-scales of gravitational perturbation satisfy a certain relation, the perturbation will grow in one component and decay in the other. Specific calculations are made for the development of inhomogeneity in a universe consisting of two collisionless gases. It is found that as long as the densities of the Jeans lengths of the two components satisfy the relations ϱ 1 ⪡ ϱ 2 λ 1 j ⪡ λ 2 j , then, whether the initial perturbation is in component 1 or component 2, the result will be component 1 having a large degree of inhomogeneity and component 2, a small one. If the invisible matter is mainly neutrino with a finite rest-mass, then the above result can be used to explain the quasi-uniform distribution of the invisible matter.