Quantum Geometrodynamics with intrinsic time development and momentric variables is our new discovery. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl Curvature Hypothesis, and thermodynamic and gravitational 'arrows of time' point in the same direction. Ricci scalar potential corresponding to Einstein's General Relativity emerges as a zero-point energy contribution. A new set of fundamental commutation relations without Planck's constant emerges from the unification of Gravitation and Quantum Mechanics.
Classically, since the contribution from the Weyl curvature tensor drops out from the full Riemann curvature tensor and therefore doesn't show up in the Einstein Equation; therefore, to determine the initial conditions of the Universe in General Relativity, one has to be supplemented with the Weyl Curvature Conjecture as proposed by Penrose; in the intrinsic time formalism, this fixed by the Cotton-York tensor and the simultaneous vanishing of the ground state. This result result in FRW cosmology with constant curvature(homogenous and isotropic) slicing. At the full fledge quantum theory, this semi-classical state exactly corresponds to the saddle point, expansion around this saddle point naturally gives raises to the primordial 1/k^3 scale invariant tensor perturbation modes plus possible non-Gaussianities.
Here are the links to some of our research works:
Intrinsic Time Gravity and the Lichnerowicz-York Equation, Niall OMurchadha, Chopin Soo and Hoi-Lai Yu; Class. Quantum Grav. 30 (2013) 095016(Editorial Board Highlight of the year)
General Relativity without paradigm of space-time covariance, and resolution of the problem of time, Chopin Soo and Hoi Lai Yu; Prog. Theor. Exp. Phys. 2014, 013E01
Intrinsic time quantum geometrodynamics, Eyo Ita, Chopin Soo and Hoi Lai Yu; Prog. Theor. Exp. Phys. 2015, 083E01
New Commutation Relations for Quantum Gravity, Chopin Soo and Hoi Lai Yu; Chinese J. Phys., 53(2015), 110106-1(Special issues on the occasion of the hundredth years of GR)
New Looks at Gauge Theories and Quantum Gravity, Hoi Lai Yu(Invited talk at LeCospa ll, 2015)