Averaging Dynamics of Scalar Field-Matter Interacting Models in Anisotropic Universes: The Locally Rotationally Symmetric Bianchi I Spacetime

TL;DR

This paper analyzes the dynamics of an anisotropic universe model with scalar fields and matter interactions, using averaging theory to understand the solution space and conditions for regular evolution.

Contribution

It introduces a novel application of averaging theory to anisotropic scalar field-matter models, revealing how Hubble parameter modulation influences system behavior and singularity prevention.

Findings

Hubble parameter acts as a perturbation parameter controlling oscillations.

Conditions on interaction parameters ensure regular, singularity-free evolution.

As the perturbation parameter decreases, the system approaches asymptotic behavior.

Abstract

We consider an anisotropic cosmological model based on the locally rotational Bianchi I spacetime, incorporating a scalar field and a non-zero cosmological interaction term. The framework of averaging theory is employed to study the associated non-linear differential equations. Through a qualitative analysis of the gravitational field equations, we obtain valuable insights into the structure of the solution space for the anisotropic scalar field model with a generalized harmonic potential. The interaction between the scalar field and matter is described by a general expression that depends on the Hubble parameter, the time derivative of the scalar field, and the energy densities of cold dark matter and dark energy. This formulation involves real parameters that modulate the interaction, as well as a coupling constant with the dimensions of the Hubble parameter. We show that the Hubble parameter serves as a time-dependent perturbation parameter, controlling the discrepancy between the full system and its time-averaged counterpart. As this parameter decreases, both systems converge to the same asymptotic behaviour. This enables the suppression of oscillatory effects, significantly simplifying the dynamical analysis. Finally, we identify conditions on the interaction parameters that ensure the regularity of the system's evolution by preventing the emergence of singularities.