Gravity Sources in a Quantum Milne Universe

TL;DR

This paper develops a quantum cosmology model based on a sliced Milne universe, describing its structure, symmetries, and implications for total universe momentum, angular momentum, and energy, using advanced mathematical frameworks.

Contribution

It introduces a quantum Milne universe model with a novel slice and ray structure, incorporating Gelfand-Naimark unitarity, fiber bundles, and symmetry principles to explain cosmological properties.

Findings

Total universe angular momentum vanishes

Total universe momentum vanishes

Total universe energy vanishes

Abstract

A quantum-cosmology-suited sliced Milne spacetime, located inside a 'big-bang' forward lightcone, comprises the interiors of a sequence of 4-dimensional slices whose invariant 'age' width is at Planck scale. The age of any lightcone-interior point is its Minkowski distance from the lightcone vertex, but excluded from the spacetime of a 'quantum Milne universe' (QMU) are 3-dimensional slice-separating, ray-carrying hyperboloids. Each (fixed-age) slice boundary houses a Gelfand-Naimark unitarily Lorentz-transformable cosmological-Fock-space ray-a sum of tensor products of complex normed fiber-bundle 'source' functions. Each bundle is a unit 3-sphere (fiber) over an invariantly metricized 3-hyperboloid (base space). The evolving QMU comprises a slice-interior sequence (each interior a 4-manifold) and a ray sequence housed by the slice-separating 3-manifolds. Throughout each slice interior, the preceding ray specifies classical-field reality. Action, of elsewhere-prescribed slice-traversing Feynman paths, determines any ray after the first from its predecessor. QMUs related by a global 7-parameter Lie-group symmetry transformation, at fixed age, are equivalent--the same quantum universe. This 'cosmological relativity' implies vanishing of total universe angular momentum (Mach's principle) as well as of total universe momentum. Milne's cosmological principle accompanies vanishing of total-universe energy. (Seven 'Noether-conserved' quantities separately aggregate to zero).