Chaplygin gas quantum universe in the presence of the cosmological constant

Details Chaplygin gas quantum universe in the presence of the cosmological constant Chaplygin gas quantum universe in the presence of the cosmological constant

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010gregr..42..745p&link_type=abstract

General Relativity and Gravitation, Volume 42, Issue 4, pp.745-762

Mathematics

Logic

Quantum Cosmology, Chaplygin Gas, Spectral Method

Scientific paper

We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant. We apply the Schutz’s variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the effective cosmological constant during the transition from the early times to the late times. For the case of an effective negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale factors never tend to the singular point, we have an initial indication that this model may not have singularities at the quantum level.

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