Dust and Radiation Quantum Perfect Fluid Cosmology : Selection of Time Variable

TL;DR

This paper investigates the quantum cosmology of dust and radiation perfect fluids, demonstrating how different choices of time variables can align quantum expectation values with classical General Relativity predictions.

Contribution

It introduces a method to select dynamical time variables in quantum perfect fluid cosmology, ensuring consistency with classical cosmological behavior.

Findings

Expectation value of scale factor matches classical predictions with proper time variable selection.

Different perfect fluid systems can have distinct time variables that yield consistent quantum-classical correspondence.

Exact solutions to the Wheeler-DeWitt equation are obtained and used to analyze quantum cosmological models.

Abstract

We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutz variational formalism to describe perfect fluid and selected the conjugate coordinate of perfect fluid be dynamical variable. After quantization and solving the Wheeler-DeWitt equation can obtain the exact solution. By superposition of the exact solution, we obtained one wave packets and used it to compute the expectation value of the scale factor. We found that if one select different dynamical variable be the time variable in each of these two systems, the expectation value of the scale factor of these two systems can fit in with the prediction of General Relativity. Therefore we thought that the selection of reference time can be different for different quantum perfect fluid systems.