Geodetic Brane Gravity

TL;DR

This paper develops a Hamiltonian framework for geodetic brane gravity, revealing its potential to naturally incorporate dark matter, address the problem of time, and facilitate quantum cosmology calculations without extra fields.

Contribution

It introduces a new canonical formalism with constraints and BRST symmetry for geodetic brane gravity, highlighting its novel features and advantages over traditional models.

Findings

Derivation of quadratic Hamiltonian with matter coupling

Identification of intrinsic dark matter component

Resolution of the 'problem of time' in quantum cosmology

Abstract

Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields {lambda, P_{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 bracket formalism. The algebra of the first class constraints is calculated, and the 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 lambda being a vanishing (degenerate) eigenvalue.