A singularity theorem based on spatial averages

J M M SENOVILLA

F\'{\i}sica Te\'orica, Universidad

del Pa\'{\i}s Vasco, Apartado 644, 48080 Bilbao, Spain

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 Universes, expanding everywhere with a

non-vanishing spatial average of the matter variables, show severe

geodesic incompletness in 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.

Keywords. Raychaudhuri equation; singularity-free cosmologies;

singularity theorems.

PACS Nos 04.20.Cv; 04.20.Dw; 98.80.Jk