Phantom energy mediates a long-range repulsive force

Scalar field models with nonstandard kinetic terms have been proposed in the context of k inflation, of Born-Infeld Lagrangians, of phantom energy and, more in general, of low-energy string theory. In general, scalar fields are expected to couple to matter inducing a new interaction. In this Letter I derive the cosmological perturbation equations and the Yukawa correction to gravity for such general models. I find three interesting results: first, when the field behaves as phantom energy (equation of state less than -1), then the coupling strength is negative, inducing a long-range repulsive force; second, the dark-energy field might cluster on astrophysical scales; third, applying the formalism to a Brans-Dicke theory with a general kinetic term it is shown that its Newtonian effects depend on a single parameter that generalizes the Brans-Dicke constant.