(N+1)-dimensional quantum mechanical model for a closed universe

A quantum mechanical model for an (N + I)-dimensional universe arising from a quantum fluctuation is outlined. (3 + I) dimensions are a closed, infini tely expanding universe, and the remaining N - 3 dimensions are compact, Th e (3 + I)noncompact dimensions are modeled by quantizing a canonical Hamilt onian description of a homogeneous isotropic universe. It is assumed that g ravity and the strong-electroweak (SEW) force had equal strengths in the in itial state. Inflation occurred when the compact (N - 3)-dimensional space collapsed after a quantum transition from the initial state of the universe during its evolution to the present state where gravity is much weaker tha n the SEW force. The model suggests the universe has no singularities and t he large size of our present universe is determined by the relative strengt h of gravity and the SEW force today. A small cosmological constant, result ing from the zero-point energy of the scalar field corresponding to the com pact dimensions, makes the model universe expand forever.