Cosmological model with non-minimally coupled fermionic field

¹  Departamento de Física, Universidade Federal do Paraná - Caixa Postal 19044, 81531-990 Curitiba, Brazil
²  Faculdades Integradas Espírita - Rua Tobias de Macedo Jr. 333, 82010-340 Curitiba, Brazil

Received: 28 July 2007
Accepted: 26 October 2007

Abstract

A model for the Universe is proposed whose constituents are: a) a dark energy field modeled by a fermionic field non-minimally coupled with the gravitational field, b) a matter field which consists of pressureless baryonic and dark matter fields and c) a field which represents the radiation and the neutrinos. The coupled system of Dirac's equations and Einstein field equations is solved numerically by considering a spatially flat homogeneous and isotropic Universe. It is shown that the proposed model can reproduce the expected red-shift behaviors of the deceleration parameter, of the density parameters of each constituent and of the luminosity distance. Furthermore, for small values of the red-shift the constant which couples the fermionic and gravitational fields has a remarkable influence on the density and deceleration parameters.