The perfect-fluid cosmology in the (1 + d+D)-dimensional Kaluza-Klein space-times for an arbitrary barotropic equation of state p = (γ - 1)ρ is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. In the first case of the stiff fluid γ = 2 we exactly solve the Wheeler-DeWitt equation when the d space is flat. After the superposition of the solutions the wave-packet function is obtained exactly. We analyze the Bohmian trajectories of the finalstage wave-packet functions and show that the scale functions of the flat d spaces and the compact D spaces will eventually evolve into the nonzero finite values. In the second case of γ = 2, we use the approximated wave function 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 = ∞.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics