https://doi.org/10.1140/epjc/s10052-021-09802-5
Regular Article - Theoretical Physics
Time-averaging axion-like interacting scalar fields models
1
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
2
International Center for Cosmology, Charusat University, 388421, Anand, Gujarat, India
3
Dirección de Investigación y Postgrado, Universidad de Aconcagua, Pedro de Villagra 2265, 7630367, Vitacura, Santiago, Chile
4
Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Avda. Angamos 0610, Antofagasta, Chile
5
Shanghai Jiao Tong University, 800 Dongchuan RD, Minhang District, 200240, Shanghai, China
Received:
9
July
2021
Accepted:
1
November
2021
Published online:
27
November
2021
In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields 
and 
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.
© The Author(s) 2021
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