Bimetric MOND gravity

By Mordehai Milgrom. 2009

181 citations recorded by the source corpus.

A new relativistic formulation of MOND is advanced, involving two metrics as independent degrees of freedom: the MOND metric g{sub {mu}}{sub {nu}}, to which alone matter couples, and an auxiliary metric g-circumflex{sub {mu}}{sub {nu}}. The main idea hinges on the fact that we can form tensors from the difference of the Levi-Civita connections of the two metrics, C{sub {beta}}{sub {gamma}}{sup {alpha}}={gamma}{sub {beta}}{sub {gamma}}{sup {alpha}}-{gamma}-circumflex{sub {beta}}{sub {gamma}}{sup {alpha}}, and these act like gravitational accelerations. In the context of MOND, we can form dimensionless 'acceleration' scalars and functions thereof (containing only first derivatives) from contractions of a{sub 0}{sup -1}C{sub {beta}}{sub {gamma}}{sup {alpha}}. I look at a subclass of bimetric MOND theories governed by the action I=-(16{pi}G){sup -1}{integral}[{beta}g{sup 1/2}R+{alpha}g-circumflex{sup 1/2}R-circumflex-2(gg-circumflex){sup 1/4}f({kappa})a{sub 0}{sup 2} M({upsilon}-tilde/a{sub 0}{sup 2})]d{sup 4}x+I{sub M}(g{sub {mu}}{sub {nu}},{psi}{sub i})+I-circumflex{sub M}(g-circumflex{sub {mu}}{sub {nu}},{chi}{sub i}), with {upsilon}-tilde as a scalar quadratic in the C{sub {beta}}{sub {gamma}}{sup {alpha}}, {kappa}=(g/g-circumflex){sup 1/4}, I{sub M} as the matter action, and allow for the existence of twin matter that couples to g-circumflex{sub {mu}}{sub {nu}} alone. Thus, gravity is modified not by modifying the elasticity of the space-time in which matter lives, but by the interaction between that space-time and the auxiliary one. In particular, I concentrate on themore » interesting and simple choice {upsilon}-tilde{proportional_to}g{sup {mu}}{sup {nu}}(C{sub {mu}}{sub {lambda}}{sup {gamma}}C{sub {nu}}{sub {gamma}}{sup {lambda}}-C{sub {mu}}{sub {nu}}{sup {gamma}}C{sub {lambda}}{sub {gamma}}{sup {lambda}}). This theory introduces only one new constant, a{sub 0}; it tends simply to general relativity (GR) in the limit a{sub 0}{yields}0 and to a phenomenologically valid MOND theory in the nonrelativistic limit. The theory naturally gives MOND and 'dark energy' effects from the same term in the action, both controlled by the MOND constant a{sub 0}. In regards to gravitational lensing by nonrelativistic systems-a holy grail for relativistic MOND theories-the theory predicts that the same potential that controls massive-particle motion also dictates lensing in the same way as in GR: Lensing and massive-particle probing of galactic fields will require the same 'halo' of dark matter to explain the departure of the present theory from GR. This last result can be modified with other choices of {upsilon}-tilde, but lensing is still enhanced and MOND-like, with an effective logarithmic potential.« less

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1654e3dfaa239c70faaa7eba55fb81fc85dcf706

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Citations in the corpus

Modified Gravity and Cosmology (2011, background): “More phenomenologically, Bekenstein’s relativistic formulation of Milgrom’s Modified Newtonian Dynamics (MoND) has provided a fresh impetus for new study: What was previously a rule of thumb for how weak gravitational fields might behave in regions of low acceleration, was suddenly elevated to a the”
Local-Group tests of dark-matter concordance cosmology - Towards a new paradigm for structure formation (2010, background): “…would be purely defined by the baryonic matter distribution in non-DM models indeed would naturally explain the later finding based on a large sample of galaxies by Disney et al. (2008), Gentile et al. (2009), and Milgrom (2009a) that disc galaxies appear to be governed by a single parameter.”
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action (2013, background): “To name a few, f(R) theories of gravity [4], generalise Scalar-Tensor theories [5], TeVeS [6] and MOND [7–9] (see also [10] and references therein for a thorough presentation).”
Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions (2011, background): “Again, it is mandatory to stress that the formulation of BIMOND sketched above is actually far from unique and can be suitably parametrized to yield a whole class of BIMOND theories with various phenomenological behaviors [312, 317, 318].”
Galaxies as simple dynamical systems: observational data disfavor dark matter and stochastic star formation (2014, methodology): “In one formulation of Milgromian dynamics, bimond [50], the acceleration is relative to another metric in the form of the subtraction of two Christoffel symbols.”
Quasi-linear formulation of MOND (2009, methodology): “The density ρp is what was called in Milgrom (2009a) “the surrogate mass density”, and was used as an approximation for the phantom density of the nonlinear Poisson theory.”