Ostrogradski approach for the Regge-Teitelboim type cosmology

Abstract

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.

11 pages, 2 figures, accepted for publication in Phys. Rev. D

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• Embedding theory as new geometrical mimetic gravity
• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Removing Ostrogradski ghost from degenerate gravity theories
• The approach to gravity as a theory of embedded surface
• Quantum modified Regge-Teitelboim cosmology
• Hamiltonian analysis for linearly acceleration-dependent Lagrangians
• Quantum charged rigid membrane
• Gauge symmetry and Virasoro algebra in quantum charged rigid membrane -- a first order formalism
• The Hilbert Lagrangian and Isometric Embedding: Tetrad Formulation of Regge-Teitelboim Gravity
• BRST symmetry for Regge-Teitelboim based minisuperspace models
• Higher order curvature terms in Born-Infeld type brane theories
• Covariant approach of perturbations in Lovelock type brane gravity
• Hamilton-Jacobi approach for Regge-Teitelboim cosmology
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Hydrogen-like Spectrum of Spontaneously Created Brane Universes with deSitter Ground State
• Weak field limit for embedding gravity
• Ostrogradsky-Hamilton approach to geodetic brane gravity
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• Explicit isometric embeddings of collapsing dust ball
• Canonical formulation of embedding gravity in a form of General Relativity with dark matter
• Hamilton-Jacobi approach for linearly acceleration-dependent Lagrangians
• Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
• Holographic relationships in Lovelock type brane gravity
• A Lagrangian form of tangent forms
• The Unruh effect for higher derivative field theory
• Investigation of Faddeev variant of embedding theory
• Modified Hamiltonian formalism for Regge Teitelboim Cosmology
• Investigations In Higher Derivative Field Theories