Intrinsic Time Geometrodynamics

A discourse on time, gravity, and the universe that takes the reader through the subtleties of time, the origin of the universe, and physical evolution in Einstein's theory and its extensions. Can time and causality remain fundamental when the classical ideal of spacetime becomes a concept of limited applicability in quantum gravity? A thorough exposition on the canonical framework of Einstein's theory and its extensions reveals the synergy between gravitation and the cosmic clock of our expanding universe that renders time concrete, physical, and comprehensible. In conjunction with a paradigm shift from four-covariance to just spatial diffeomorphism invariance, causal time-ordering of the quantum state of the universe and its evolution in cosmic time become meaningful. The quantum state of the universe is the embodiment of our shared past, present, and future. The advocated framework prompts natural extensions and improvements to Einstein's theory. A salient feature is the addition of a Cotton-York term to the physical Hamiltonian. Besides bringing improved ultraviolet convergence, this radically changes the solution to the initial data problem and the quantum origin of the universe. It lends support to the quantum beginning of the universe as an exact Chern-Simons Hartle-Hawking state that features Euclidean-Lorentzian instanton tunneling. A signature of this state is that it manifests, at the lowest order approximation, scale-invariant two-point correlation function for transverse-traceless quantum metric fluctuations. This initial quantum state also implies, at the level of expectation values, a low-entropy hot smooth Robertson-Walker beginning that is in accord with Penrose's Weyl Curvature Hypothesis. Consequently, the gravitational arrow of time of increasing spatial volume and the thermodynamic second law arrow of time of increasing entropy concur as our universe expands and ages.