Inhomogeneous solutions in cosmology

Abstract

The standard cosmological solutions of Einstein's equations of general relativity describe a fluid that is homogeneous and isotropic in density and pressure. These solutions, often called the Friedmann–Robertson–Walker solutions, are believed to be good descriptions of the universe at the present time. But early on, processes connected with particle physics and quantum field theory may have caused localized inhomogeneities, and recently some new kinds of solution of Einstein's equations have been found, which may describe such regions. In one solution being studied by Wesson and Ponce de Leon (Phys. Rev. D: Part. Fields, 39, 420 (1989)), the density is still uniform but the pressure is nonuniform about a centre. The mass is given by a relation that looks like the familiar Newtonian relation m = (4/3)πR3ρ. However, the solution has other properties that are quite strange (e.g. a region of negative pressure and a kind of dipolar geometry). It is not known if solutions like this are merely mathematical curiosities or imply something about the behaviour of real matter in extreme situations.