Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lema\^itre-Robertson-Walker models

TL;DR

This paper uses averaging methods to analyze scalar field cosmologies with matter in LRS Bianchi III and open FLRW models, showing that late-time behavior can be predicted by simplified averaged systems.

Contribution

It introduces an averaging approach to determine the asymptotic dynamics of scalar field cosmologies with matter in specific anisotropic and open universe models.

Findings

Late-time attractors include flat spacetime, matter-dominated universes, and scaling solutions.

Averaged systems accurately predict the late-time behavior of the original dynamical systems.

Numerical simulations confirm the smoothing of oscillations as the Hubble parameter approaches zero.

Abstract

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $\gamma$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $\gamma$ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein-Gordon (KG) equation can be controlled and smoothed out as the Hubble factor $H$ - acting as a time-dependent perturbation parameter - tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.