Scalar Field Cosmologies and the Initial Space-Time Singularity

TL;DR

This paper investigates the initial singularity in scalar field cosmologies, showing that most models have a simple past asymptotic structure similar to massless scalar fields, with implications for the initial value problem.

Contribution

It demonstrates that a broad class of scalar field cosmologies share a common asymptotic structure near the initial singularity, extending understanding of initial conditions in cosmology.

Findings

Most models have a regular past asymptotic structure.

A family of solutions corresponds to massless scalar field cosmologies.

Solutions not in this family are of measure zero.

Abstract

The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical systems approach which may readily be generalised to more complicated space-times. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous 1-1 correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realised by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial value problem is briefly discussed.