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Assuming the space dimension is not constant, but varies with the expansionof 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 thedimension of space at the Planck time. The standard FRW model corresponds tothe limiting case $C \to +\infty$. We study the Wheeler-De Witt equation andthe wave function of the Universe and the probability density in our modelUniverse. In the limit of constant space dimension, our wave functionapproaches to the Hartle-Hawking wave function or to a modified Linde wavefunction.Comment: 37 pages, 7 ps figuers, latex fil

Model universe with variable space dimension: Its dynamics and wave function