Stephani-Schutz quantum cosmology

Abstract

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 Schrödinger 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.

6 pages, 4 figures, 1 table, to appear in PLB

References in corpus (2)

• Using Spectral Method as an Approximation for Solving Hyperbolic PDEs
• Schrödinger-Wheeler-DeWitt equation in chaplygin gas FRW cosmological model

Cited by in corpus (4)

• Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid
• Quantum cosmology with varying speed of light: canonical approach
• Perfect fluid quantum Universe in the presence of negative cosmological constant
• Signature change from Schutz's canonical quantum cosmology and its classical analogue