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–Lemaître–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.
Highlights
IntroductionIn references [149,154] scalar field cosmologies with arbitrary potential and with arbitrary coupling to matter were studied
We have studied systems that can be expressed in the standard form (37), where H is the Hubble parameter and is positive strictly decreasing in t and limt→∞ H (t) = 0
Defining Z = 1 − Σ2 − Ω2 − Ωk which is monotonic as H → 0, due to there is a continuous function α such that Z = −H Z α + O H 2 it was proved that sign of 1−Σ2 −Ω2−Ωk is invariant as H → 0
Summary
In references [149,154] scalar field cosmologies with arbitrary potential and with arbitrary coupling to matter were studied. This paper is a sequel of [149,154], where asymptotic methods and averaging theory [155,156,157,158,159,160,161] were used to obtain relevant information about solution’s space of scalar field cosmologies with generalized harmonic potential: (i) in vacuum, (ii) in presence of matter. 4 we apply averaging methods to analyze periodic solutions of a scalar field with self-interacting potentials within the class of generalized harmonic potentials [148].
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