A model Universe with variable space dimension: its dynamics and wave function

Details A model Universe with variable space dimension: its dynamics and wave function A model Universe with variable space dimension: its dynamics and wave function

1999-02-14

arxiv.org/abs/gr-qc/9902043v1

Phys.Rev. D60 (1999) 123512

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

37 pages, 7 ps figuers, latex file

Scientific paper

10.1103/PhysRevD.60.123512

Assuming the space dimension is not constant, but varies with the expansion of the Universe, a Lagrangian formulation for a toy model Universe is given. There is a free paremeter in the theory, $C$, with which we can fix the dimension of space at the Planck time. The standard FRW model corresponds to the limiting case $C \to +\infty$. We study the Wheeler-De Witt equation and the wave function of the Universe and the probability density in our model Universe. In the limit of constant space dimension, our wave function approaches to the Hartle-Hawking wave function or to a modified Linde wave function.

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