Isotropy theorem for cosmological vector fields
  We consider homogeneous abelian vector fields in an expanding universe. We
find a mechanical analogy in which the system behaves as a particle moving in
three dimensions under the action of a central potential. In the case of
bounded and rapid evolution compared to the rate of expansion, we show by
making use of the virial theorem that for arbitrary potential and polarization
pattern, the average energy-momentum tensor is always diagonal and isotropic
despite the intrinsic anisotropic evolution of the vector field. For simple
power-law potentials of the form V=\lambda (A^\mu A_\mu)^n, the average
equation of state is found to be w=(n-1)/(n+1). This implies that vector
coherent oscillations could act as natural dark matter or dark energy
candidates. Finally, we show that under very general conditions, the average
energy-momentum tensor of a rapidly evolving bounded vector field in any
background geometry is always isotropic and has the perfect fluid form for any
locally inertial observer.
