  We consider the cosmological implications of a gravitational theory
containing two vector fields coupled minimally to gravity as well as a
generalized Chern-Simons term that couples the two vector fields. 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 will show that there is 6 degrees of freedom
propagate on top of de Sitter space-time, two tensor polarizations and four
degrees of freedom related to two massless vector fields interacting with each
other via Chern-Simons interaction term. We also investigate in detail the
behavior of the geometric and physical parameters of a homogeneous and
anisotropic Bianchi type I Universe, by using both analytical and numerical
methods, by assuming that the matter content of the Universe can be described
by the stiff causal and pressureless dust fluid equations of state. The time
evolution of the Bianchi type I Universe strongly depends on the initial
conditions of the physical and geometrical quantities, as well as on the
numerical values of the model parameters. Two important observational
parameters, the mean anisotropy parameter, and the deceleration parameter, are
also studied in detail, 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 and exponentially accelerating, de Sitter type, phase.
