On the Nature of Singularities in Plane Symmetric Scalar Field Cosmologies

TL;DR

This paper investigates the initial singularity in plane symmetric scalar field cosmologies, showing it is crushing, velocity dominated, and that the Kretschmann scalar diverges, preventing past extension through a Cauchy horizon, with some subclasses having isotropic singularities.

Contribution

It demonstrates the nature of the singularity in these cosmologies and identifies subclasses with isotropic singularities, advancing understanding of their geometric properties.

Findings

Singularity is crushing and velocity dominated.

Kretschmann scalar diverges uniformly near the singularity.

Some subclasses have isotropic singularities.

Abstract

The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the Kretschmann scalar diverges uniformly as it is approached. The last fact means in particular that a maximal globally hyperbolic spacetime in this class cannot be extended towards the past through a Cauchy horizon. A subclass of these spacetimes is identified for which the singularity is isotropic.