Chaplygin gas quantum universe in the presence of the cosmological constant |
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Authors: | Pouria Pedram and Shahram Jalalzadeh |
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Institution: | 1.Plasma Physics Research Center, Science and Research Campus,Islamic Azad University,Tehran,Iran;2.Department of Physics,Shahid Beheshti University, G. C.,,Tehran,Iran |
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Abstract: | 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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