Zahra Haghani, Tiberiu Harko, Hamid Reza Sepangi and Shahab Shahidi
arXiv:1604.04837 [gr-qc]
Publication year: 2016

We consider a vector-tensor gravitational model in which the action for the minimally coupled vector field also contains additional terms quadratic in the Maxwell tensor derivatives, and corresponds to the covariant form of the so-called Bopp-Podolsky electrodynamics. A term describing the non-minimal coupling between the cosmological mass current and the four-potential of the vector field as well as the self-interaction potential of the vector field is also included in the action. From a cosmological point of view we interpret the vector field as describing dark energy, which is responsible for the late acceleration of the Universe. The gravitational field equations of the model and the equations describing the evolution of the vector field are obtained and their Newtonian limit is investigated. The cosmological implications of a Bopp-Podolsky type dark energy term are investigated for a Friedmann-Robertson-Walker homogeneous and isotropic geometry for two models, corresponding to the absence and presence of the self-interaction potential of the field, respectively. The redshift evolution of the scale factor, the matter energy density, the Hubble function, the deceleration parameter and the field potential are obtained for both cases. In the presence of the vector type dark energy with quadratic terms in the Maxwell tensor derivatives the Universe ends its evolution in an exponentially accelerating vacuum de Sitter state, independently of the presence or absence of the self-interaction potential.