Averaging generalized scalar field cosmologies III: Kantowski--Sachs and closed Friedmann--Lemaître--Robertson--Walker models

Abstract

Scalar field cosmologies with a generalized harmonic potential and a background matter given by a barotropic Equation of State (EoS) are investigated for Kantowski-Sachs metric and closed Friedmann-Lemaître-Robertson-Walker (FLRW) metrics. Using methods from the Theory of Averaging of Nonlinear Dynamical Systems and numerical simulations it is proved that the full equations of the time dependent system and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest timeaveraged system determines the future asymptotic of the full system. In particular, for Kantowski-Sachs metric the late-time attractors of the full and time-averaged systems are: two anisotropic contracting solutions for 0 ≤ γ < 2: a non-Flat LRS Kasner Bianchi I and a Taub (flat LRS Kasner) and the flat matter dominated FLRW universe if 0 ≤ γ ≤ 2 3 (mimicking de Sitter, quintessence or zero acceleration solutions). For closed FLRW metric the late-time attractors are: the flat Friedman Einstein-de-Sitter solution for 0 < γ < 1, the flat matter dominated FLRW universe for 0 ≤ γ ≤ 2 3 (mimicking de Sitter, quintessence or zero acceleration solutions), and a matter dominated contracting isotropic solution for 1 < γ < 2. With this approach the oscillations entering the system through Klein-Gordon equation can be controlled and smoothed out as a relevant time-dependent perturbative parameter goes monotonically to zero for a finite time t < t * . The region where the perturbation parameter changes its monotony to monotonic increasing is analyzed by a discrete symmetry and by using proper variables that brings infinity to a finite interval.

Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models

“…In all metrics, the matter dominated flat FLRW universe represents quintessence fluid if 0 < γ < 2 3 . Continuing the Program "Averaging Generalized Scalar Field Cosmologies", the cases: (II) Bianchi I and Flat FLRW model and (III) Kantowski-Sachs and Closed FLRW are respectively studied in two companion papers [146,147]. In [146] it is used the same approach used here.…”

“…However, in the case (III) this approach is not valid given that H is not necessarily monotonically decreasing to zero, and it can change its sign. Therefore, we have developed an alternative procedure in [147].…”

“…This research program -named "Averaging Generalized Scalar Field Cosmologies"-has three steps according to the three cases of study: (I) Bianchi III and Open FLRW model, (II) Bianchi I and Flat FLRW model and (III) Kantowski-Sachs and Closed FLRW. This paper is devoted to the case I and cases II and III will be studied in two companion papers [146,147]. The paper is organized as follows.…”

Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models

“…In all metrics, the matter dominated flat FLRW universe represents quintessence fluid if 0 < γ < 2 3 . This paper is devoted to the case (II) and case (III) will be studied in a companion paper [62].…”