Reconstructing the parameter space of non-analytical cosmological fixed points

TL;DR

This paper introduces a numerical scheme to analyze the parameter space of complex cosmological models with non-analytical fixed points, demonstrated on a scalar-vector dark energy model, aiding the study of intricate dynamical systems.

Contribution

The paper presents a general numerical method to explore the parameter space of dynamical systems with non-analytical fixed points in cosmology.

Findings

Identified accelerated attractors without analytical fixed point expressions.

Provided a template for numerical analysis of complex dynamical systems.

Demonstrated the method on a scalar-vector dark energy model.

Abstract

Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a set of autonomous first-order differential equations. The fixed points of this autonomous set encode the asymptotic evolution of the model. Usually, these points can be written as analytical expressions for the variables in terms of the parameters of the model, which allows a complete characterization of the corresponding parameter space. However, a thoroughly analytical treatment is impossible in some cases. In this work, we give an example of a dark energy model, a scalar field coupled to a vector field in an anisotropic background, where not all the fixed points can be analytically found. Then, we put forward a general scheme that provides a numerical description of the parameter space. This allows us to find interesting accelerated attractors of the system with no analytical representation. This work may serve as a template for the numerical analysis of highly complicated dynamical systems.