Around MOND: Lagrangians, Hubble Equations, Perturbations and External Field Effect

Abstract

The MOdified Newtonian Dynamics (MOND) is presented here, as well as a theory that can be linked to it: the theory of the Aether, a four-vector field breaking Lorentz invariance. The form of its Lagrangian is studied, then basic equations of the theory are rederived in a detailed way, and calculated for different metrics, exploring the impact of non-zero spatial terms of the Aether. A brief attempt of making the Aether Lagrangian depend on a scalar field is presented. An analytic solving of a galaxy model with an external field is described, which highlights the MONDian external field effect that breaks the strong equivalence principle.