An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables

TL;DR

This paper introduces a (1+1)-dimensional quantum gravity model that treats observables as explicitly evolvable, linking it to string theory in curved backgrounds, and proposes a scheme to address the problem of time and the cosmological constant.

Contribution

It presents a novel quantization scheme for inhomogeneous quantum gravity with explicit observables and offers insights into the cosmological constant problem.

Findings

Model corresponds to a string in curved background

Solution to the problem of time via quasi-Heisenberg operators

Potential resolution of the cosmological constant problem

Abstract

An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt equation and the "particle on a sphere" type of the gauge condition is suggested. In the quantization scheme considered, the "problem of time" is solved by building of the quasi-Heisenberg operators acting in a space of solutions of the Wheeler-DeWitt equation and the normalization of the wave function corresponds to the Klein-Gordon type. To analyze the physical consequences of the scheme, a (1+1)-dimensional background space is considered for which a classical solution is found and quantized. The obtained estimations show the way to solution of the cosmological constant problem, which consists in compensation of the zero-point oscillations of the matter fields by the quantum oscillations of the scale factor. Along with such a compensation, a slow global evolution of a background corresponding to an universe expansion exists.