Wave Functional of the Universe and Time

TL;DR

This paper proposes a quantum gravity framework based on a wave functional of the universe, incorporating a quantum least action principle and a covariant description of cosmic evolution with an invariant time parameter.

Contribution

It introduces a new formulation of quantum gravity using a wave functional invariant under covariant transformations and defines an invariant evolutionary time parameter.

Findings

Wave functional is invariant under general covariant transformations.

Evolution of the universe described with a generalized geodesic time.

Formulation aligns quantum theory with classical Einstein gravity principles.

Abstract

A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the corresponding action operator. Its solution, the wave functional, is an invariant of general covariant transformations of space-time. In the new formulation, the history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions, which makes this description close to the formulation of the principle of general covariance in the classical theory of Einstein's gravity. In the new formulation of the quantum theory, an invariant parameter of the evolutionary time of the universe is defined, which is a generalization of the classical geodesic time, measured by a standard clock along time-like geodesics.