Effective field theory reproducing the MOND phenomenology based on a non-Abelian Yang-Mills graviphoton

TL;DR

This paper introduces an effective field theory based on a non-Abelian Yang-Mills gauge field that reproduces MOND phenomenology through gravitational polarization, without arbitrary functions, and involves Lorentz invariance violation at low accelerations.

Contribution

It presents a novel effective field theory model that reproduces MOND behavior via a non-Abelian gauge field and gravitational polarization, linking MOND to a new sector of the standard model.

Findings

Reproduces deep MOND limit without arbitrary functions

Involves a non-Abelian Yang-Mills gauge field (graviphoton)

Restores covariance with a scalar Khronon field

Abstract

Motivated by the phenomenology of MOND, we propose a theory based on a fundamental non Abelian Yang-Mills gauge field with gravitational coupling constant (a "graviphoton") emerging in a regime of weak acceleration, i.e. below the MOND acceleration scale. Using the formalism of the effective field theory and invoking a mechanism of gravitational polarization of the dark matter medium, we show that generic solutions of this theory reproduce the deep MOND limit without having to introduce in an ad hoc way an arbitrary function in the action. In this framework, MOND is due to the existence of a new sector of the standard model of particle physics. Furthermore, the model involves a violation of the local Lorentz invariance in the low acceleration regime. We show how to restore the general covariance of the model by adding one gravitational degree of freedom in the form of the scalar Khronon field.