Vector dark energy models with quadratic terms in the Maxwell tensor derivatives

TL;DR

This paper explores a vector-tensor gravity model with quadratic Maxwell tensor derivatives, analyzing its cosmological implications for anisotropic universes and showing how vector dark energy influences isotropization.

Contribution

It introduces a novel vector-tensor model with quadratic Maxwell derivatives and investigates its cosmological evolution and isotropization effects in anisotropic universes.

Findings

Vector dark energy affects the universe's anisotropic evolution.

Self-interacting potential accelerates isotropization.

Numerical solutions show complex dynamical behavior.

Abstract

We consider a vector-tensor gravitational model with terms quadratic in the Maxwell tensor derivatives, called the Bopp-Podolsky term. 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 Bianchi type I homogeneous and anisotropic geometry for two models, corresponding to the absence and presence of the self-interacting potential of the field, respectively. The time evolutions of the Hubble function, of the matter energy density, of the shear scalar, of the mean anisotropy parameter, and of the deceleration parameter, respectively, as well as the field potentials are obtained for both cases by numerically integrating the cosmological evolution equations. In the presence of the vector type dark energy with quadratic terms in the Maxwell tensor derivatives, depending on the numerical values of the model parameters, the Bianchi type I Universe experiences a complex dynamical evolution, with the dust Universes ending in an isotropic phase. The presence of the self-interacting potential of the vector field significantly shortens the time interval necessary for the full isotropization of the Universe.