Gauge vector–tensor gravity


Gauge vector–tensor gravity is a relativistic generalization of Mordehai Milgrom's modified Newtonian dynamics paradigm where gauge fields cause the MOND behavior. The former covariant realizations of MOND such as the Bekenestein's tensor–vector–scalar gravity and the Moffat's scalar–tensor–vector gravity attribute MONDian behavior to some scalar fields. GVT is the first example wherein the MONDian behavior is mapped to the gauge vector fields.
The main features of GVT can be summarized as follows:
Its dynamical degrees of freedom are:
The physical geometry, as seen by particles, represents the Finsler geometry–Randers type:
This implies that the orbit of a particle with mass can be derived from the following effective action:
The geometrical quantities are Riemannian. GVT, thus, is a bi-geometric gravity.

Action

The metric's action coincides to that of the Einstein–Hilbert gravity:
where is the Ricci scalar constructed out from the metric. The action of the gauge fields follow:
where L has the following MOND asymptotic behaviors
and represent the coupling constants of the theory while are the parameters of the theory and

Coupling to the matter

Metric couples to the energy-momentum tensor. The matter current is the source field of both gauge fields. The matter current is
where is the density and represents the four velocity.

Regimes of the GVT theory

GVT accommodates the Newtonian and MOND regime of gravity; but it admits the post-MONDian regime.

Strong and Newtonian regimes

The strong and Newtonian regime of the theory is defined to be where holds:
The consistency between the gravitoelectromagnetism approximation to the GVT theory and that predicted and measured by the Einstein–Hilbert gravity demands that
which results in
So the theory coincides to the Einstein–Hilbert gravity in its Newtonian and strong regimes.

MOND regime

The MOND regime of the theory is defined to be
So the action for the field becomes aquadratic. For the static mass distribution, the theory then converts to the AQUAL model of gravity with the critical acceleration of
So the GVT theory is capable of reproducing the flat rotational velocity curves of galaxies. The current observations do not fix which is supposedly of order one.

Post-MONDian regime

The post-MONDian regime of the theory is defined where both of the actions of the are aquadratic. The MOND type behavior is suppressed in this regime due to the contribution of the second gauge field.