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Slightly Bimetric Gravitation

The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance. Next we slightly weaken the assumptions of universal coupling and gauge invariance, obtaining a larger ``slightly bimetric'' class of theories, in which the Euler-Lagrange equations depend only on a curved metric, matter fields, and the determinant of the flat metric. The theories are equivalent to generally covariant theories with an arbitrary cosmological constant and an arbitrarily coupled scalar field, which can serve as an inflaton or dark matter. The question of the consistency of the null cone structures of the two metrics is addressed. A difficulty for Logunov's massive gravitation on this front is noted.