Averaging generalized scalar field cosmologies IV: locally rotationally symmetric Bianchi V model

TL;DR

This paper investigates scalar field cosmologies with generalized potentials in anisotropic Bianchi V models, demonstrating that oscillations can be controlled and solutions simplified through time-averaging techniques.

Contribution

It provides new insights into Bianchi V scalar field cosmologies and shows how time-dependent perturbations can be used to analyze asymptotic behaviour.

Findings

Hubble parameter acts as a perturbation controlling error magnitude

Time-averaged solutions match full-system asymptotic behaviour

Oscillations can be smoothed out to simplify analysis

Abstract

This research focuses on scalar field cosmologies with a generalized harmonic potential. Our attention is centred on the anisotropic LRS Bianchi I and III metrics, Bianchi V metrics, and their isotropic limits. We provide a comprehensive overview of the first two metrics classes and offer new findings for Bianchi V metrics. We show that the Hubble parameter is a time-dependent perturbation parameter that controls the magnitude of the error between full-system and time-averaged solutions as it decreases, such that those complete and time-averaged systems have the same asymptotic behaviour. Therefore, oscillations entering the system can be controlled and smoothed out, which simplifies the problem at hand.