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

TL;DR

This paper uses averaging methods to analyze the late-time behavior of scalar field cosmologies with matter, showing that oscillations can be smoothed out and identifying key attractors depending on the matter's barotropic index.

Contribution

It applies the theory of averaging to scalar field cosmologies with LRS Bianchi I and flat FLRW metrics, revealing the asymptotic dynamics and attractors.

Findings

Late-time attractors include flat quintessence dominated FLRW universe and Einstein-de Sitter solution.

Time-averaged systems accurately predict the late-time behavior of the original systems.

Oscillations in the Klein-Gordon equation can be controlled and smoothed out as the Hubble parameter tends to 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 the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) metrics 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, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $\gamma$, the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein-Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter $H$ - acting as time-dependent perturbation parameter - tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.