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 Qf ( 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 _ { DE } closer to -1 .
This alleviates the problem of observational incompatibility of uncoupled models in which w _ { DE } significantly deviates from -1 .
The maximum values of w _ { DE } reached during the matter era are bounded from the CDM no-ghost condition of future de Sitter solutions .