Improving relativistic modified Newtonian dynamics with Galileon k-mouflage

We propose a simple field theory reproducing MOND phenomenology at galaxy scale, while predicting negligible deviations from general relativity at small scales thanks to an extended Vainshtein ("k-mouflage'') mechanism induced by a covariant Galileon-type Lagrangian. The model passes all solar-system tests, including those of local Lorentz invariance, and its anomalous forces in binary pulsars are vanishingly small. The large-distance behavior is obtained as in Bekenstein's tensor-vector-scalar model, but with several simplifications. In particular, no fine-tuned function is needed to interpolate between the MOND and Newtonian regimes, and the vector field may be nondynamical. The field equations depend on second (and lower) derivatives, and thus avoid the generic Ostrogradski instabilities. We also underline why the proposed model is particularly efficient within the class of covariant Galileons.