Cosmic Time and General Relativity

Eyo ITa, Chopin Soo, Hoi Lai 2017  arXiv:1711.01394  

In an ever-expanding spatially closed universe, the fracti
onal change of the volume is the preemi-
nent intrinsic time interval to describe evolution in Gener
al Relativity. With this additional physical
input, the constraints are no longer first class, but can in fa
ct be turned into a set of second class
constraints when the physical degrees of freedom (d.o.f.) a
re identified with transverse-traceless ex-
citations. A true physical Hamiltonian for intrinsic time e
volution emerges, together with a reduced
phase space with two d.o.f. apposite to functional integral
methods and perturbative quantization.
Freed from the first class Dirac algebra, deformation of the H
amiltonian constraint is permitted,
and natural extension of the Hamiltonian while maintaining
spatial diffeomorphism invariance leads
to a theory with Cotton-York term as the ultra-violet comple
tion of Einstein’s General Relativity.