A candidate for relativistic MOND with successful cosmology was proposed by using a Lorentz-violating vector field in Einstein's gravity. However, we show that considering the dynamic nature of the vector field makes it challenging to realize the MOND phenomenology. Removing the dynamic part as a physical condition results in inconsistencies in the cosmological context. Attempts to remove the dynamic aspect by redefining time coordinate lead to non-Newtonian hydrodynamics, while the dynamic nature persists in Poisson's equation. We study the evolution of density perturbations in the baryon-vector field system using both post-Newtonian approximations and relativistic perturbation theory. Our results show that the behavior differs from what we expect in the non-relativistic MOND proposal.
References:
arXiv: 2404.06584
arXiv: 2410.10205