  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.
