On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field

TL;DR

This paper investigates the long-term behavior of locally rotationally symmetric Bianchi type III cosmological models with a massive scalar field, revealing their asymptotic expansion patterns and matter dominance at late times.

Contribution

It provides the first detailed analysis of future asymptotics for these models, including the dominant metric and scalar field behavior, supported by analytical and numerical evidence.

Findings

The metric expands forever with one direction logarithmically and others at power-law rates.

Energy density approaches zero but the models remain matter dominated.

Results are supported by a conjecture with strong analytical and numerical backing.

Abstract

We analyse spatially homogenous cosmological models of locally rotationally symmetric Bianchi type III with a massive scalar field as matter model. Our main result concerns the future asymptotics of these spacetimes and gives the dominant time behaviour of the metric and the scalar field for all solutions for late times. This metric is forever expanding in all directions, however in one spatial direction only at a logarithmic rate, while at a power-law rate in the other two. Although the energy density goes to zero, it is matter dominated in the sense that the metric components differ qualitatively from the corresponding vacuum future asymptotics. Our results rely on a conjecture for which we give strong analytical and numerical support. For this we apply methods from the theory of averaging in nonlinear dynamical systems. This allows us to control the oscillations entering the system through the scalar field by the Klein-Gordon equation in a perturbative approach.