Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

Abstract

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$ γ 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 $$\gamma $$ γ 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.

Time-averaging axion-like interacting scalar fields models

“…Perturbations methods and averaging methods were used, for example, in [142][143][144][145][146][147][148][149][150]. One idea is to construct a timeaveraged version of the original system, solving it; the oscillations of the original system are smoothed out [150].…”

“…One idea is to construct a timeaveraged version of the original system, solving it; the oscillations of the original system are smoothed out [150]. This can be achieved for homogeneous metrics where the Hubble parameter H plays the role of a time dependent perturbation parameter which controls the magnitude of the error between the solutions of the full and the time-averaged problems whenever H is monotonic and sign invariant, H is positive strictly decreasing in t and lim t→∞ H (t) = 0 [147,148,151]. Therefore, it is possible to obtain information about the largetime behavior of more complicated systems via an analysis of the simpler averaged system equations using dynamical systems techniques.…”

“…In the Refs. [147][148][149] a research program "Averaging generalized scalar field cosmologies" was started. It consisted of using asymptotic methods and averaging theory [158] to explore the solution's space of scalar field cosmologies with generalized harmonic potential in vacuum or minimally coupled to matter.…”

“…It consisted of using asymptotic methods and averaging theory [158] to explore the solution's space of scalar field cosmologies with generalized harmonic potential in vacuum or minimally coupled to matter. As a difference with [147,148], where the Hubble parameter was used as a timedependent perturbation parameter, in [149] systems where Hubble scalar is not monotonic were studied.…”

“…In this paper we generalize the program initiated in [147][148][149] to two-fluid cosmological models. To this goal, we analyze an axion-like coupled scalar fields model following Ref.…”