Geodetic Brane Gravity

Geodetic brane gravity treats the universe as an extended object evolving geodetically within a higher dimensional flat background. In this paper we derive the quadratic Hamiltonian of the brane by introducing a new pair of canonical fields $\lambda,P_{\lambda}$. This causes second class constraints to enter the game, and calls for the use of Dirac Brackets. The algebra of first class constraints is calculated, and the BRST generator of the brane universe is of rank 1. The Einstein case, associated with $\lambda$ being a vanishing (degenerate) eigenvalue, can be treated only as a limiting case. At the quantum level, the road is open for canonical quantization, or functional integral quantization. The main advantages of GBG are: It contains an intrinsic, geometrically originated 'dark matter' components. It contains an intrinsic solution to the 'problem of time' with the aid of the 'bulk' time coordinate. It enables calculation of meaningful probabilities within quantum cosmology without any additional scalar field