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We studied the expectation value of the scale factor in radiation and dustquantum perfect fluid cosmology. We used Schutz variational formalism todescribe perfect fluid and selected the conjugate coordinate of perfect fluidbe dynamical variable. After quantization and solving the Wheeler-DeWittequation can obtain the exact solution. By superposition of the exact solution,we obtained one wave packets and used it to compute the expectation value ofthe scale factor. We found that if one select different dynamical variable bethe time variable in each of these two systems, the expectation value of thescale factor of these two systems can fit in with the prediction of GeneralRelativity. Therefore we thought that the selection of reference time can bedifferent for different quantum perfect fluid systems.Comment: 5 pages, revtex4 typ

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