Time-averaging axion-like interacting scalar fields models

TL;DR

This paper investigates a cosmological model with two interacting axion-like scalar fields, using novel dynamical variables and averaging methods to analyze late-time behavior and oscillations.

Contribution

It introduces a new dynamical systems approach with time-averaging techniques to study oscillating scalar fields in cosmology, demonstrating equivalence of time-averaged and original system dynamics.

Findings

Time-averaged systems share the same late-time dynamics as original systems.

Oscillations can be effectively analyzed using averaging methods.

Numerical simulations support the theoretical results.

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.