Cosmological post-Newtonian approximation of a Lorentz-violating vector field (2503.20151v1)

Abstract: A candidate for relativistic MOND with successful cosmology was proposed by using a Lorentz-violating vector field in Einstein's gravity. We show that the dynamic nature of the vector field makes it challenging to realize the MOND. Only in the stationary limit, thus excluding cosmological situations, one can achieve the MOND limit. We study the evolution of density perturbations in the baryon-vector field system using both post-Newtonian approximation and relativistic perturbation theory. Our results show that the behavior differs from what we expect in the non-relativistic MOND proposal, i.e., the faster growth of structures in the MOND regime.