Relativistic gravitation theory for the modified Newtonian dynamics paradigm
Abstract
The modified Newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the postNewtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an a priori vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar, and a 4vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small. We calculate the β and γ parameterized postNewtonian coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. To the extent that MOND successfully describes dynamics of a system, the new theory’s predictions for lensing by that system’s visible matter will agree as well with observations as general relativity’s predictions made with a dynamically successful dark halo model. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar, and vector waves.
 Publication:

Physical Review D
 Pub Date:
 October 2004
 DOI:
 10.1103/PhysRevD.70.083509
 arXiv:
 arXiv:astroph/0403694
 Bibcode:
 2004PhRvD..70h3509B
 Keywords:

 95.35.+d;
 04.80.Cc;
 95.30.Sf;
 98.62.Sb;
 Dark matter;
 Experimental tests of gravitational theories;
 Relativity and gravitation;
 Gravitational lenses and luminous arcs;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 ReVTeX and 3 eps figures