Abstract
We consider the cosmological implications of a gravitational theory containing two vector fields coupled via a generalized Chern–Simons term. One of the vector fields is the usual Maxwell field, while the other is a constrained vector field with constant norm included in the action via a Lagrange multiplier. The theory admits a de Sitter type solution, with healthy cosmological perturbations. We also show that there are seven degrees of freedom that propagate on top of de Sitter space-time, consisting of two tensor polarizations, four degrees of freedom related to the two vector fields, and a scalar degree of freedom that makes one of the vector fields massive. We investigate the cosmological evolution of Bianchi type I space-time, by assuming that the matter content of the Universe can be described by the stiff and dust. The cosmological evolution of the Bianchi type I Universe strongly depends on the initial conditions of the physical quantities, as well as on the model parameters. The mean anisotropy parameter, and the deceleration parameter, are also studied, and we show that independently of the matter equation of state the cosmological evolution of the Bianchi type I Universe always ends in an isotropic de Sitter type phase.
Highlights
An alternative way to produce an accelerated expanding Universe is to add some light degrees of freedom to the theory of general relativity
Much work has been done in the context of scalar field cosmology, including inflationary [27,28,29] and dark energy models [30,31,32]
An interesting scalar field theory was proposed, which has higher than second order terms in the time derivative interactions in the action, their equations of motion remains at most second order [33,34,35]
Summary
An alternative way to produce an accelerated expanding Universe is to add some light degrees of freedom to the theory of general relativity. The cosmological implications of the Horndeski type theories have been extensively investigated in the literature [36,37,38,39,40,41,42,43] Another interesting possibility is to add a vector degree of freedom to the theory of Einstein general relativity. We are going to investigate the cosmological implications of the Chern–Simons term as a representative of dark energy effect To this end, we will restore the Lorentz invariance of the theory by promoting the constant vector kμ to a dynamical field and impose a constant norm constraint by adding this property by a Lagrange multiplier. In the last section we discuss our results and conclude
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