(N + 1)-Dimensional Quantum Mechanical Model for a Closed Universe

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Abstract

A quantum mechanical model for an (N + 1)-dimensional universe arising from a quantum fluctuation is outlined. (3 + 1) dimensions are a closed, infinitely expanding universe, and the remaining N - 3 dimensions are compact. The (3 + 1) noncompact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed that gravity and the strong-electroweak (SEW) force had equal strengths in the initial 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 than the SEW force. The model suggests the universe has no singularities and the large size of our present universe is determined by the relative strength of gravity and the SEW force today. A small cosmological constant, resulting from the zero-point energy of the scalar field corresponding to the compact dimensions, makes the model universe expand forever.

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