Connecting relativistic MOND theories with mimetic gravity

We find a connection between relativistic Modified Newtonian Dynamics (MOND) theories and (scalar) mimetic gravity. We first demonstrate that any relativistic MOND model featuring a unit-timelike vector field, such as TeVeS or Aether-scalar-tensor theory, can be embedded within a conformal/disformal-invariant framework. Gauge fixing the conformal/disformal symmetry amounts to imposing a constraint on the norm of the vector, the scalar field or the cross contraction. Notably, we find that these constraints can be interchanged as long as the vector and scalar fields remain timelike. This means that relativistic MOND theories may be recasted as a mimetic gravity theory. Lastly, by constructing the fundamental building blocks of a conformal-invariant scalar-vector-tensor theory, we establish a new framework for developing relativistic MOND theories. This perspective offers deeper insight into how non-invertible disformal transformations and conformal/disformal symmetries serve as fundamental principles in constructing viable alternatives to dark matter.