A new approach on the stability analysis in ELKO cosmology

TL;DR

This paper introduces a dynamical system approach to analyze the stability of ELKO field and dark matter interactions, providing conditions that could help address the cosmic coincidence problem.

Contribution

It develops a new stability analysis method for ELKO-dark matter systems without specifying the potential, identifying parameter conditions for stable cosmological solutions.

Findings

Stable fixed points depend on parameters $eta$ and $eta$

Conditions for decay of ELKO into dark matter derived

Potential constraints can alleviate the cosmic coincidence problem

Abstract

In this work it has been developed a new approach to study the stability of a system composed by an ELKO field interacting with dark matter, which could give some contribution in order to alleviate the cosmic coincidence problem. It is assumed that the potential which characterizes the ELKO field is not specified, but it is related to a constant parameter $\delta$. The strength of the interaction between matter and ELKO field is characterized by a constant parameter $\beta$ and it is also assumed that both ELKO field as matter energy density are related to their pressures by equations of state parameters $\omega_\phi$ and $\omega_m$, respectively. The system of equations is analysed by a dynamical system approach. It has been found the conditions of stability between the parameters $\delta$ and $\beta$ in order to have stable fixed points for the system for different values of the equation of state parameters $\omega_\phi$ and $\omega_m$, and the results are presented in form of tables. The possibility of decay of ELKO field into dark matter or vice versa can be read directly from the tables, since the parameters $\delta$ and $\beta$ satisfy some inequalities. It allows us to constrain the potential assuming that we have a stable system for different interactions terms between the ELKO field and dark matter. The cosmic coincidence problem can be alleviated for some specific relations between the parameters of the model.