### 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.

Original language | English |
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Article number | 104021 |

Journal | Physical Review D |

Volume | 97 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2018 May 15 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*97*(10), [104021]. https://doi.org/10.1103/PhysRevD.97.104021

}

*Physical Review D*, vol. 97, no. 10, 104021. https://doi.org/10.1103/PhysRevD.97.104021

**Cosmic time and reduced phase space of general relativity.** / Ita, Eyo Eyo; Soo, Chopin; Yu, Hoi Lai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Cosmic time and reduced phase space of general relativity

AU - Ita, Eyo Eyo

AU - Soo, Chopin

AU - Yu, Hoi Lai

PY - 2018/5/15

Y1 - 2018/5/15

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.97.104021

DO - 10.1103/PhysRevD.97.104021

M3 - Article

AN - SCOPUS:85048085830

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 104021

ER -