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Bimetric MOND gravity

A new relativistic formulation of MOND is advanced, involving two metrics as independent degrees of freedom: the MOND metric g_mn, to which alone matter couples, and an auxiliary metric g*_mn. The main idea hinges on the fact that we can form tensors from the difference, C^a_bc, of the Levi-Civita connections of the two metrics, and these act like gravitational accelerations. In the context of MOND we can form dimensionless `acceleration' scalars, and functions thereof, from contractions of C^a_bc/a0. I look at a class of bimetric MOND theories governed by an action with the gravitational Lagrangian density b sqrt(g)R+a sqrt(g*) R* -2(gg*)^{1/4}f(k)a0^2M(U/a0^2), and with matter actions I(g_mn,psi)+I*(g*_mn,chi), with U a scalar quadratic in the C^a_bc, k=(g/g*)^{1/4}, and allowing for the existence of twin matter, chi, that couples to g*_mn alone. In particular, I concentrate on one interesting and simple choice of the scalar U. This theory introduces only one new constant, a0; it tends simply to General Relativity in the limit a0 goes to 0, and to a phenomenologically valid MOND theory in the nonrelativistic limit. The theory naturally gives MOND and "dark energy" eff