Non commutative quantum spacetime with topological vortex states, and dark matter in the universe

TL;DR

This paper explores how non-commutative geometry and topological vortex solutions in quantum spacetime could explain dark matter within cosmological models, linking advanced mathematical structures to fundamental universe components.

Contribution

It introduces a novel approach using non-commutative topology and vortex solutions to model dark matter in the universe at grand unified energy scales.

Findings

Topological vortex solutions can represent dark matter.

Non-commutative geometry provides a framework for early universe physics.

The model connects with existing grand unified theories.

Abstract

Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There is a variety of physics possible till the nucleosynthesis epoch is reached. The use of topology and non commutative geometry in cosmology is a recent approach. This paper considers the possibility of topological solutions of a vortex kind given by non commutative structures. These are interpreted as dark matter, with the grand unified Yang-Mills field theory energy scale used to describe its properties. The relation of the model with other existing theories is discussed.