N + 1 dimensional quantum mechanical model for a closed universe

TL;DR

This paper proposes a quantum mechanical model of an N+1 dimensional universe originating from quantum fluctuations, explaining its expansion, the role of forces, and the absence of singularities through compact dimensions and force strength dynamics.

Contribution

It introduces a novel quantum model of a higher-dimensional universe with compact dimensions, linking force strengths and quantum transitions to cosmic evolution.

Findings

Universe has no singularities in the model.

Large universe size is determined by force strength ratios.

Small cosmological constant leads to eternal expansion.

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) non-compact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed gravity and the strong-electro-weak (SEW) forces had equal strength in the initial state. Inflation occurred when the compact N -3 dimensional space collapsed after a quantum transition from the initial state of the univers, 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.