Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-08-30
Phys.Lett.B655:91-96,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages, 4 figures, 1 table, to appear in PLB
Scientific paper
10.1016/j.physletb.2007.08.077
We study the Stephani quantum cosmological model in the presence of a cosmological constant in radiation dominated Universe. In the present work the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to Wheeler-DeWitt equations which can be cast in the form of Schr\"odinger equations for the scale factor. We find their eigenvalues and eigenfunctions by using the Spectral Method. Then we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor, which is found to oscillate between non-zero finite maximum and minimum values. Since the expectation value of the scale factor never tends to the singular point, we have an initial indication that this model may not have singularities at the quantum level.
Gousheh Siamak S.
Jalalzadeh Shahram
Pedram Pouria
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