A new approach on the stability analysis in ELKO cosmology

A. P. dos Santos Souza; S. H. Pereira; J. F. Jesus

doi:10.1140/epjc/s10052-015-3260-9

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2015) 75: 36
https://doi.org/10.1140/epjc/s10052-015-3260-9

Regular Article - Theoretical Physics

A new approach on the stability analysis in ELKO cosmology

A. P. dos Santos Souza¹, S. H. Pereira¹^* and J. F. Jesus²

¹ Departamento de Física e Química, Faculdade de Engenharia de Guaratinguetá, UNESP-Univ. Estadual Paulista “Júlio de Mesquita Filho”, Av. Dr. Ariberto Pereira da Cunha 333-Pedregulho, Guaratinguetá, SP, 12516-410, Brazil
² Universidade Estadual Paulista “Júlio de Mesquita Filho”, Campus Itapeva Rua Geraldo Alckmin 519, Vila N. Sra. de Fátima, Itapeva, SP, 18409-010, Brazil

^* e-mail: shpereira@gmail.com

Received: 29 August 2014
Accepted: 5 January 2015
Published online: 29 January 2015

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 and matter energy density are related to their pressures by equations of state parameters $\omega _\phi$ and $\omega _m$ , respectively. The system of equations is analyzed 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 the 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.