A singularity theorem based on spatial averages

Abstract

Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables are severely geodesically incomplete to the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.

Corrections made in the main theorem and related places. 16 pages, no figures. Invited contribution to the Pramana special issue, dedicated to A K Raychaudhuri, on "the Raychaudhuri Equation and its Role in Modern Cosmology" (Edited by Naresh Dadhich, Pankaj Joshi and Probir Roy). Final version to be published

Cited by in corpus (2)

• The Raychaudhuri equations: a brief review
• On the genericity of spacetime singularities