On the stability and causality of scalar-vector theories
  Various extensions of standard inflationary models have been proposed
recently by adding vector fields. Because they are generally motivated by
large-scale anomalies, and the possibility of statistical anisotropy of
primordial fluctuations, such models require to introduce non-standard
couplings between vector fields on the one hand, and either gravity or scalar
fields on the other hand. In this article, we study models involving a vector
field coupled to a scalar field. We derive restrictive necessary conditions for
these models to be both stable (Hamiltonian bounded by below) and causal
(hyperbolic equations of motion).
