Cosmic Time and General Relativity

Eyo Ito, Chopin Soo and Hoi Lai Yu 2017   

In an ever-expanding spatially closed universe, the fractional change of the volume is the preemi- nent intrinsic time interval to describe evolution in General Relativity. With this additional physical input, the constraints are no longer first class, but can in fact be turned into a set of second class constraints when the physical degrees of freedom (d.o.f.) are identified with transverse-traceless ex- citations. A true physical Hamiltonian for intrinsic time evolution 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 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 ultra-violet completion of Einstein’s General Relativity.