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 the 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 Einstein's theory and the cosmic clock of our expanding universe that render time 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 wave function 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 ultra-violet convergence, this radically changes the initial data problem of Einstein's theory and the possible initial state of the universe. It lends support to the origin of the universe as an exact Chern-Simons-Hartle-Hawking state that exhibits semiclassical Euclidean-Lorentzian instanton tunneling. A signature of the initial state is that it manifests, at the lowest order approximation, scale-invariant transverse-traceless quantum metric fluctuations. With this hot smooth Robertson-Walker beginning which satisfies Penrose's Weyl Curvature Hypothesis, the thermodynamic arrow of time of increasing entropy and the cosmic arrow of time of our expanding universe concur.