Vector theories in cosmology
  This article provides a general study of the Hamiltonian stability and the
hyperbolicity of vector field models involving both a general function of the
Faraday tensor and its dual, $f(F^2,F\tilde F)$, as well as a Proca potential
for the vector field, $V(A^2)$. In particular it is demonstrated that theories
involving only $f(F^2)$ do not satisfy the hyperbolicity conditions. It is then
shown that in this class of models, the cosmological dynamics always dilutes
the vector field. In the case of a nonminimal coupling to gravity, it is
established that theories involving $R f(A^2)$ or $Rf(F^2)$ are generically
pathologic. To finish, we exhibit a model where the vector field is not diluted
during the cosmological evolution, because of a nonminimal vector
field-curvature coupling which maintains second-order field equations. The
relevance of such models for cosmology is discussed.
