Cosmological model with non-minimally coupled fermionic fieldM. O. Ribas1, 2, F. P. Devecchi1 and G. M. Kremer1
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 in final form 26 October 2007; published January 2008
published online 19 November 2007
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.
98.80.-k - Cosmology.
95.36.+x - Dark energy.
95.35.+d - Dark matter (stellar, interstellar, galactic, and cosmological).
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