Cosmological perturbations of a relativistic MOND theory

A relativistic MOND theory, promising in reproducing cosmology as well as the MOND phenomenology in the low acceleration regime, was recently proposed. We present the post-Newtonian (PN) approximation and relativistic perturbation equations of this theory in cosmological context. The PN equations are presented to 1PN order and perturbation equations are presented in fully-nonlinear and exact forms. The gauge issues are clarified. The 1PN equations and linear perturbation equations are presented without imposing temporal gauge conditions. We show that to 0PN order baryon perturbation grows faster in the MOND regime. The MOND field can be interpreted as a fluid with specific equation of state without anisotropic stress, and the Jeans criterion is derived for the MOND field.