Gauge vector–tensor gravity

Gauge vector–tensor gravity[1] (GVT) is a relativistic generalization of Mordehai Milgrom's modified Newtonian dynamics (MOND) paradigm[2] 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:

  • Two gauge fields: ;
  • A metric, .

Details

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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

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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

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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

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

Strong and Newtonian regimes

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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

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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[3] 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

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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.

See also

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References

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  1. ^ Exirifard, Qasem (27 August 2013). "GravitoMagnetic force in modified Newtonian dynamics". Journal of Cosmology and Astroparticle Physics. 2013 (8): 046. arXiv:1107.2109. Bibcode:2013JCAP...08..046E. doi:10.1088/1475-7516/2013/08/046.
  2. ^ Milgrom, M. (1 July 1983). "A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis". The Astrophysical Journal. 270: 365. Bibcode:1983ApJ...270..365M. doi:10.1086/161130.
  3. ^ Bekenstein, J.; Milgrom, M. (1 November 1984). "Does the missing mass problem signal the breakdown of Newtonian gravity?". The Astrophysical Journal. 286: 7. Bibcode:1984ApJ...286....7B. doi:10.1086/162570.