Time-averaging axion-like interacting scalar fields models

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.

Automated summary

This paper studies a cosmological model inspired by axionic matter, involving two scalar fields interacting through a added potential term. By introducing new variables and a dimensionless time scale, the resulting dynamics are explored. The analysis of oscillations using methods from the theory of averaging nonlinear systems is motivated by difficulties in standard approaches, ultimately proving the consistency of time-dependent systems and their time-averaged counterparts in late-time dynamics.