The Self-Accelerating Universe with Vectors in Massive Gravity

We explore the possibility of realising self-accelerated expansion of the Universe taking into account the vector components of a massive graviton. The effective action in the decoupling limit contains an infinite number of terms, once the vector degrees of freedom are included. These can be re-summed in physically interesting situations, which result in non-polynomial couplings between the scalar and vector modes. We show there are self-accelerating background solutions for this effective action, with the possibility of having a non-trivial profile for the vector fields. We then study fluctuations around these solutions and show that there is always a ghost, if a background vector field is present. When the background vector field is switched off, the ghost can be avoided, at the price of entering into a strong coupling regime, in which the vector fluctuations have vanishing kinetic terms. Finally we show that the inclusion of a bare cosmological constant does not change the previous conclusions and it does not lead to a ghost mode in the absence of a background vector field.