Dust and radiation quantum perfect fluid cosmology: selection of time variable

We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutzs variational formalism to describe the perfect fluid and selected the conjugate coordinate of the perfect fluid to be the dynamical variable. After quantization and solving the Wheeler-DeWitt equation we obtained an exact solution. By superposition of exact solutions, we obtained one wave packet and used it to compute the expectation value of the scale factor. We found that if one selects a different dynamical variable being 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 a reference time can be different for different quantum perfect fluid systems.