Space-times with constant vacuum energy density and a conformal Killing vector

Abstract

We find a class of solutions to the Einstein field equations with constant vacuum energy density (''cosmological constant'') that has a similarity symmetry of the second kind. We show this symmetry to be a global conformal symmetry. Nontrivial analytic solutions are given and one in particular (exhibiting intrinsic symmetry) is shown to evolve to a nonempty Robertson-Walker space-time with ''steady-state'' metric. This is found to be due to particle production associated with the negative matter pressure that is required by the assumed symmetry. These models can describe, classically, an origin of the Universe in terms of particle production from the vacuum, driving an exponential (de Sitter) expansion. This solution is inhomogeneous and anisotropic, but tends to homogeneity and isotropy at early times and large distances, and at late times and small distances. The solution therefore corresponds to the outward motion of a spherical disturbance which distorts the local homogeneity and isotropy in an asymptotically homogeneous and isotropic universe. The limiting homogeneous and isotropic forms are discussed.