Geodetic brane gravity

Within the framework of geodetic brane gravity, the universe is described as a four-dimensional extended object evolving geodetically in a higher-dimensional flat background. In this paper, by introducing a new pair of canonical fields [Formula Presented] we derive the quadratic Hamiltonian for such a brane universe; the inclusion of matter then resembles minimal coupling. Second class constraints enter the game, invoking the Dirac brackets formalism. The algebra of the first class constraints is calculated, and the Becchi-Rouet-Stora transformation (BRST) generator of the brane universe turns out to be rank [Formula Presented] At the quantum level, the road is open for canonical and/or functional integral quantization. The main advantages of geodetic brane gravity are (i) it introduces an intrinsic, geometrically originated, “dark matter” component, (ii) it offers, owing to the Lorentzian bulk time coordinate, a novel solution to the “problem of time”, and (iii) it enables calculation of meaningful probabilities within quantum cosmology without any auxiliary scalar field. Intriguingly, the general relativity limit is associated with [Formula Presented] being a vanishing (degenerate) eigenvalue.