Bimetric Theory of Gravity (Bigravity)

In General
* History: 1934, Born-Infeld theory can be considered as a form of bimetric theory (according to Moffat); 1973–1974, New version proposed by N Rosen; 1979–1995, J Moffat's non-symmetric gravitation theory; 1992, J Bekenstein's treatment of gravitational lensing and MOND; 1998–2003, Clayton-Moffat scalar-vector-tensor theory.
* Setup: If we call g_ab the gravitational metric, which controls the speed of gravity, a second metric is given by

g'_ab = g_ab + (B/c²) _a b ,

where B is a positive number (which will probably be renormalized by quantum effects), and a scalar field coupled to gravity (g_ab); All other fields couple to the "matter metric" g'_ab, whose light cones therefore control their propagation.
* Properties: One of the main differences with general relativity is that it does not produce black holes.

Phenomenology > s.a. anomalous acceleration; variation of constants; [cosmological models].
* Variation of c: The different metrics that apply to gravitation and other fields give rise to an effectively changing speed of light; Depending on whether one uses electromagnetic or other (say, gravitational) waves to study the early universe, one gets that the other speed changes in time (the ratio c_grav/c_gamma is dimensionless and meaningful).
* Cosmology: If we set the gravitational c_grav to be constant, the electromagnetic c_gamma will vary and increase close to the big bang; This solves the horizon problem without using inflation (although the Friedmann equation changes too).
@ References: Moffat ap/00, IJMPD(03)gq/02 [variable c and supernovas]; Moffat qp/02 [entanglement]; Kopeikin & Ni gq/06-in [laser ranging delay]; Kopeikin gq/05 [speed of light and gravity]; Petit & D'Agostini a0712 [and cosmological acceleration].

References
@ General: Rosen AP(63), AP(66) [with flat metric], GRG(73), AP(74), & Rotbart GRG(79); Drummond PRD(01)ap/00 [dark matter alternative]; Leiter & Robertson gq/01/GRG [?]; Pitts & Schieve GRG(01)gq ["slightly bimetric"], gq/01-in [consistency]; Blas et al PRD(07).
@ Related topics: Damour & Kogan PRD(02) [non-linear, L_eff]; Blas et al CQG(06) [solutions, causal structure]
@ Multigravity: Kogan ap/01-in [overview].
@ Other variants: Pitts & Schieve FP(04) [in Minkowski, same light cones].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 15 jun 2008