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

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.

18 pages

References in corpus (4)

• String theory: a perspective over the last 25 years
• Quantum gravitational decoherence of matter waves
• Canonical quantization of motion on submanifolds
• Determination of the UV cut-off from the observed value of the Universe acceleration

Cited by in corpus (6)

• Quantum mechanics allows setting initial conditions at a cosmological singularity: Gowdy model example
• AEther as an Inevitable Consequence of Quantum Gravity
• Evidence of time evolution in quantum gravity
• Cosmological singularity as an informational seed for Everything
• Illusiveness of the problem of time
• Scalar Product for a Version of Minisuperspace Model with Grassmann Variables