arXiv:0806.1913 · Journal of Cosmology and Astroparticle Physics
The quantum Stephani Universe in the vicinity of the symmetry center
Pouria Pedram
Abstract
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of 'canonical' wavepackets resulting from the solutions of a class of Wheeler–DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wavepackets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from the de Broglie–Bohm interpretation of quantum mechanics viewpoint to recover the notion of time and compare the classical and Bohmian results. We show the usage of the canonical prescription and appropriate choices of expansion coefficients to result in the suppression of the quantum potential and coincidence of classical and Bohmian results. We show that, in some cases, contrary to the Friedmann–Robertson–Walker case, the bound state solutions also exist for all positive values of the cosmological constant.