Time-averaging axion-like interacting scalar fields models

Abstract

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 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.

A perturbative analysis of interacting scalar field cosmologies

“…This example would be possible in the context of inflation from an anisotropic initial state, with transient isotropization (domination of matter or the scalar field) before reaching Minkowski solution (that is flat, isotropic, and empty of matter). As commented before, this model can describe the oscillations of the inflaton around the potential minimum during reheating after inflation, like it was described in the N-field inflation model [152] as well as in axion-like matter [148].…”

“…This approach, in which the scalar field oscillates in the minimum, before reaching a Minkowski solution, is useful for describing the oscillations of the inflaton around the potential minimum during reheating after inflation. This behavior was described in models like the N-field inflation model [152] as well as in axion-like matter [148]. The relevant calculations depend on the shape of the potential and, in particular, are quite complicated for harmonic potentials.…”

“…The averaging methods were applied extensively in [106][107][108][109][110][112][113][114][115][116] to single field scalar field cosmologies and was extended to scalar field cosmologies of two fields in [148]. New variables and dimensionless time variables were adopted, which have not been used to analyze these cosmological dynamics.…”

Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials

“…In these references, asymptotic methods and the theory of averaging in nonlinear dynamical systems are essential tools to obtain relevant information about the solution space of scalar field with generalized harmonic potential in a vacuum, and adding matter. [59][60][61][62][63][64][65][66] The amplitude-angle transformation was used in refs. [57,62,64,65,67].…”

“…[54–60] to single field scalar field cosmologies, and for scalar field cosmologies with two scalar fields which interact only gravitationally with the matter in ref. [61]. In reference, [ 62 ] scalar field cosmology with a generalized harmonic potential was investigated in Friedmann‐Lemaître‐Robertson‐Walker with flat and negative spatial curvature and for Bianchi I metrics.…”