Generalized Lagrangian Path approach to manifestly-covariant quantum gravity theory

TL;DR

This paper introduces a covariant quantum gravity framework using a Generalized Lagrangian-Path approach, demonstrating emergent gravity through statistical averaging of quantum fluctuations of the gravitational field.

Contribution

It develops a trajectory-based covariant quantum gravity theory with analytical solutions, showing how classical spacetime emerges from quantum fluctuations.

Findings

Existence of non-dispersive Gaussian-like solutions for the CQG-wave equation.

Emergent gravity phenomenon demonstrated through statistical averaging.

Background space-time metric expressed as an average over quantum fluctuations.

Abstract

A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proved to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.