Year: 2003
Type: article
Abstract: 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 ${\ensuremath{\lambda}{,P}_{\ensuremath{\lambda}}},$ 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 $1.$ 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 $\ensuremath{\lambda}$ being a vanishing (degenerate) eigenvalue.
Authors: David Karasik, Aharon Davidson
Institution: Ben-Gurion University of the Negev
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2052537950