15 - On the gravitational stability of the expanding universe

Abstract

Publisher Summary This chapter examines the gravitational stability of the expanding universe in relation to arbitrary small perturbations of the gravitational field and of the distribution of matter. The metric of a space with a constant positive curvature corresponds to a geometry on the surface of a hypersphere, embedded in an Euclidean four-dimensional space. Therefore, an arbitrary perturbation can be expanded over four-dimensional surface harmonics. In cosmological applications of the general theory of relativity, it is always assumed that the distribution of matter in space is homogeneous and isotropic; the spatial geometry is then also homogeneous and isotropic. Under this assumption, Einstein's field equations lead to two possible nonstatic models of the universe: the “closed model” with a finite space of positive curvature and the “open model” with an infinite space of negative curvature.