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Modified gravity approach based on a preferred time foliation

Abstract : We propose, in a heuristic way, a relativistic modified gravity model as an alternative to particle dark matter at galactic scales. The model is based on a postulated preferred time foliation described by a dynamical scalar field called the Khronon. In coordinates adapted to the foliation, it appears as a modification of general relativity violating local Lorentz invariance in a regime of weak gravitational fields. The model is a particular case of noncanonical Einstein-æther theory, but in which the æther vector field is hypersurface-orthogonal. We show that this model recovers the phenomenology of the modified Newtonian dynamics (MOND) in the nonrelativistic limit, and predicts the same gravitational lensing as general relativity but with a modified Poisson-type potential.
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Luc Blanchet, Sylvain Marsat. Modified gravity approach based on a preferred time foliation. Physical Review D, 2011, 84, ⟨10.1103/PhysRevD.84.044056⟩. ⟨insu-03645914⟩

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