Cosmic time and reduced phase space of General Relativity
arXiv:1711.01394 · doi:10.1103/PhysRevD.97.104021
Abstract
In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in General Relativity. The expansion of the universe serves as a subsidiary condition which transforms Einstein's theory from a first class to a second class constrained system when the physical degrees of freedom (d.o.f.) are identified with transverse traceless excitations. The super-Hamiltonian constraint is solved by eliminating the trace of the momentum in terms of the other variables, and spatial diffeomorphism symmetry is tackled explicitly by imposing transversality. The theorems of Maskawa-Nishijima appositely relate the reduced phase space to the physical variables in canonical functional integral and Dirac's criterion for second class constraints to nonvanishing Faddeev-Popov determinants in the phase space measures. A reduced physical Hamiltonian for intrinsic time evolution of the two physical d.o.f. emerges. Freed from the first class Dirac algebra, deformation of the Hamiltonian constraint is permitted, and natural extension of the Hamiltonian while maintaining spatial diffeomorphism invariance leads to a theory with Cotton-York term as the ultraviolet completion of Einstein's theory.
8 pages, replaced by published version
References in corpus (5)
Cited by in corpus (5)
- Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory
- Gravitational waves in Intrinsic Time Geometrodynamics
- Intrinsic Time in Geometrodynamics of Closed Manifolds
- Quantization of constrained systems as Dirac first class versus second class: a toy model and its implications
- Cosmic time and the initial state of the universe