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Quantum Perfect-Fluid Kaluza-Klein Cosmology

Wung-Hong Huang·I-Chin Wang
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Abstract

The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes for an arbitrary barotropic equation of state $p= n ρ$ is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. For the first case of the stiff fluid $n=1$ we exactly solve the Wheeler-DeWitt equation when the $d$ space is flat. After the superposition of the solutions we analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the flat $d$ spaces and the compact $D$ spaces will eventually evolve into finite scale functions. For the second case of $n \approx 1$, we use the approximated wavefunction in the Wheeler-DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat $d$ spaces will be expanding forever while the scale function of the contracting $D$ spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact $D$ spaces in the Kaluza-Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at $t=\infty$.

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Wung-Hong Huang, I-Chin Wang. 2007-09-03. Quantum Perfect-Fluid Kaluza-Klein Cosmology. https://doi.org/10.1142/s0217751x06031442

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