Abstract
In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields phi _1 and phi _2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein–Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.
Highlights
Even though the ΛCDM model is the most favored model by the observations [3,5,10,11], it has the following drawbacks from the theoretical point of view: (1) the value of the cosmological constant (CC) is between 60 and 120 orders of magnitude smaller than what it was estimated in Particle Physics
In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields φ1 and φ2 interacting through a term added to its potential
If the energy density of dark matter (DM) evolves in terms of redshift as ρm ∝ (1 + z)3, and the energy density of CC, ρΛ = Λ is constant, why do their energy densities have the same order of magnitude today? and why in the near past, the matter density had dropped to the same value as the dark energy (DE) density? According to the Planck 2018 results [5] we have the current values Ωm0 ≈ 0.315, ΩΛ0 ≈ 0.685, such that zeq ≈ 0.30
Summary
Even though the ΛCDM model is the most favored model by the observations [3,5,10,11], it has the following drawbacks from the theoretical point of view: (1) the value of the CC is between 60 and 120 orders of magnitude smaller than what it was estimated in Particle Physics. In the scalar field description of the DM, there are several candidates defined in terms of extension of the Standard Model like the axions, which were introduced to explain the CP violation [27]. 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. We analyze an axion-like coupled scalar fields model following Ref. Of interest in the context of natural inflation [155], where the inflation is identified with an axion-like particle This is because the shift symmetry θ → θ + C, C is a constant, protects the flatness of the potential from perturbative corrections. Near the minimum when φ nΦ∗ + ψ and |ψ| is small, V ψ where m A the axion rests mass
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