Relativistic MOND theory based on the Khronon scalar field

TL;DR

This paper proposes a relativistic modified gravity model based on a Khronon scalar field that recovers MOND behavior in the non-relativistic limit, involving Lorentz invariance violation and a preferred time foliation.

Contribution

It introduces a minimal hypersurface orthogonal model of relativistic MOND using a Khronon scalar field, offering a new interpretation of preferred time in modified gravity.

Findings

The model recovers MOND in the non-relativistic limit.

It provides a dual interpretation as a scalar field or a preferred time coordinate.

The equivalence of the two formulations is discussed.

Abstract

We investigate a model of modified gravity recovering the modified Newtonian dynamics (MOND) in the non-relativistic limit, based on the introduction of a preferred time foliation violating Lorentz invariance in the weak-field regime. Lorentz-invariance violation has been studied in the framework of Einstein-aether theory, the generalization of which, known as non-canonical Einstein-aether theory, having been proposed as a relativistic formulation of MOND. Our model can be seen as a minimal specialization to the hypersurface orthogonal case, which allows a different interpretation in terms of the preferred time : it can be either treated as a dynamical scalar field in a 4D formulation, or chosen as the time coordinate in a 3+1 formulation. We discuss the equivalence of the two points of view and the non-relativistic limit of the model.