Coupled Multi-Proca Vector Dark Energy
  We study a new class of vector dark energy models where multi-Proca fields
$A_\mu^a$ are coupled to cold dark matter by the term
$f(X)\tilde{\mathcal{L}}_{m}$ where $f(X)$ is a general function of $X\equiv
-\frac{1}{2}A^\mu_ a A^a_\mu$ and $\tilde{\mathcal{L}}_{m}$ is the cold dark
matter Lagrangian. From here, we derive the general covariant form of the novel
interaction term sourcing the field equations. This result is quite general in
the sense that encompasses Abelian and non-Abelian vector fields. In
particular, we investigate the effects of this type of coupling in a simple
dark energy model based on three copies of canonical Maxwell fields to realize
isotropic expansion. The cosmological background dynamics of the model is
examined by means of a dynamical system analysis to determine the stability of
the emergent cosmological solutions. As an interesting result, we find that the
coupling function leads to the existence of a novel scaling solution during the
dark matter dominance. Furthermore, the critical points show an early
contribution of the vector field in the form of dark radiation and a stable de
Sitter-type attractor at late times mimicking dark energy. The cosmological
evolution of the system as well as the aforementioned features are verified by
numerical computations. Observational constraints are also discussed to put the
model in a more phenomenological context in the light of future observations.
