Relativistic gravitation theory for the MOND paradigm

By J. Bekenstein. 2004

1,011 citations recorded by the source corpus.

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 post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an \textit{a priori} vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar field and a 4-vector 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 $\beta$ and $\gamma$ PPN 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.

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Citations in the corpus

Quasi-linear formulation of MOND (2009, background): “Relativistic extensions of the nonlinear Poisson theory where also propounded (see, e.g., Sanders 1997, Bekenstein 2004, 2006, Zlosnik Ferreira & Starkman 2006, 2007, Skordis 2009).”
Optimized dark matter searches in deep observations of Segue 1 with MAGIC (2013, background): “Tensor-Vector-Scalar (TeVeS) gravity is developed as the relativistic generalization of MOND [31].”
Modified Newtonian dynamics in the Milky Way (2005, background): “Bekenstein (2004) introduced the TeVeS theory of gravitation, in which the physical metric depends on the Einstein metric, a vector field, and a scalar field.”
THE SAGITTARIUS DWARF GALAXY: A MODEL FOR EVOLUTION IN A TRIAXIAL MILKY WAY HALO (2010, background): “Alternative gravity Modified Newtonian gravity (MOND; see Milgrom 1983; Bekenstein 2004) on Galactic scales has been proposed as an alternative theory to explain the flat rotation curves typical of galaxies without recourse to an extended halo of dark matter.”
NGC 3741: the dark halo profile from the most extended rotation curve (2006, methodology): “Journal compilation C© 2006 RAS, MNRAS 375, 199–212 Downloaded from https://academic.oup.com/mnras/article-abstract/375/1/199/986751 by guest on 30 July 2018 (2006) have shown not to be in contrast with the relativistic MOND theory of Bekenstein (2004): μ(x) = x 1 + x .”
Dark matter models and direct detection (2019, background): “Assuming no additional matter content, popular candidates such as TeVeS [7] give a notably worse fit to CMB”
A Direct Empirical Proof of the Existence of Dark Matter (2006, background): “In their κ map, derived in the TeVeS framework (Bekenstein 2004), the relative signal from this disk may be suppressed, but would still be easily visible with the noise levels of our reconstruction.”
The Bullet Cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter (2007, methodology): “The MOND predictions were presented for each 3 galaxy cluster, but failed to fit the data.”