Cosmic time and the initial state of the universe

TL;DR

This paper explores the role of intrinsic cosmic time in quantum gravity, proposing a paradigm shift that impacts the initial state of the universe and suggests a Chern-Simons Hartle-Hawking state with scale-invariant fluctuations.

Contribution

It introduces a new approach to quantum gravity using intrinsic time geometrodynamics and analyzes the impact of a Cotton-York term on the universe's initial state.

Findings

Quantum state as a Chern-Simons Hartle-Hawking state

Low-entropy, smooth initial universe consistent with Penrose's hypothesis

Scale-invariant quantum metric fluctuations

Abstract

The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein's theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time Geometrodynamics advocates a paradigm shift from four covariances to just spatial diffeomorphism invariance. Consequently, causal time-ordering and quantum Schrodinger-Heisenberg evolution in cosmic time become meaningful. The natural addition of a Cotton-York term to the physical Hamiltonian changes the initial data problem radically. In the classical context, this is studied with the Lichnerowicz-York equation; quantum mechanically, it lends weight to the origin of the universe as an exact Chern-Simons Hartle-Hawking state, which features Euclidean-Lorentzian instanton tunneling. At the level of expectation values, this quantum state yields a low-entropy hot smooth Robertson-Walker beginning in accord with Penrose's Weyl Curvature Hypothesis. The Chern-Simons Hartle-Hawking state also manifests transverse traceless quantum metric fluctuations, with, at the lowest approximation, scale-invariant two-point correlations as one of its defining characteristics.