Cosmic time and reduced phase space of General Relativity

TL;DR

This paper develops a reduced phase space formulation of General Relativity in an expanding universe, identifying intrinsic time with volume change, and introduces a modified Hamiltonian including a Cotton-York term for UV completion.

Contribution

It provides a novel reduced phase space approach to GR using intrinsic time and explicitly constructs a physical Hamiltonian with potential UV extensions.

Findings

Reduced phase space is related to physical variables via Maskawa-Nishijima theorems.

A physical Hamiltonian for intrinsic time evolution is derived.

Extension of the Hamiltonian includes Cotton-York term for UV completion.

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.