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

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Cited by in corpus (12)

• The 1965 Penrose singularity theorem
• A Primer on Energy Conditions
• The Raychaudhuri equations: a brief review
• Covariant kinematics and gravitational bounce in Finsler space-times
• Some generalizations of the Raychaudhuri equation
• Singularity: Raychaudhuri Equation once again
• A critical appraisal of the singularity theorems
• On the genericity of spacetime singularities
• Cosmological singularity theorems for $f(R)$ gravity theories
• How Much NEC Breaking Can the Universe Endure?
• A New Type of Singularity Theorem
• An Invitation to Lorentzian Geometry