Coupled vector dark energy
  We provide a general framework for studying the evolution of background and
cosmological perturbations in the presence of a vector field $A_{\mu}$ coupled
to cold dark matter (CDM). We consider an interacting Lagrangian of the form $Q
f(X) T_c$, where $Q$ is a coupling constant, $f$ is an arbitrary function of
$X=-A_{\mu}A^{\mu}/2$, and $T_c$ is a trace of the CDM energy-momentum tensor.
The matter coupling affects the no-ghost condition and sound speed of linear
scalar perturbations deep inside the sound horizon, while those of tensor and
vector perturbations are not subject to modifications. The existence of
interactions also modifies the no-ghost condition of CDM density perturbations.
We propose a concrete model of coupled vector dark energy with the tensor
propagation speed equivalent to that of light. In comparison to the $Q=0$ case,
we show that the decay of CDM to the vector field leads to the phantom dark
energy equation of state $w_{\rm DE}$ closer to $-1$. This alleviates the
problem of observational incompatibility of uncoupled models in which $w_{\rm
DE}$ significantly deviates from $-1$. The maximum values of $w_{\rm DE}$
reached during the matter era are bounded from the CDM no-ghost condition of
future de Sitter solutions.
