Part I. The Cosmological Vacuum from a Topological Perspective

TL;DR

This paper explores the topological structure of the cosmological vacuum, linking field energy, matter, and thermodynamics through differential forms and topological defects, offering a novel geometric perspective on fundamental physics.

Contribution

It introduces a topological framework for the cosmological vacuum using exterior differential systems, relating field properties, thermodynamics, and particle-like defects in a unified geometric approach.

Findings

Coefficients of Affine Torsion relate to field excitations like mass and charge.

Thermodynamic evolution describes the emergence of topological defects.

Potential fibers can be twisted, leading to chiral topological structures.

Abstract

This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior differential systems, which are not constrained by tensor diffeomorphic equivalences. The first postulate defines the field properties (a vector space continuum) of the Cosmological Vacuum in terms of matrices of basis functions that map exact differentials into neighborhoods of exterior differential 1-forms (potentials). The second postulate requires that the field equations must satisfy the First Law of Thermodynamics dynamically created in terms of the Lie differential with respect to a process direction field acting on the exterior differential forms that encode the thermodynamic system. The vector space of infinitesimals need not be global and its compliment is used to define particle properties as topological defects embedded in the field vector space. The potentials, as exterior differential 1-forms, are not (necessarily) uniquely integrable: the fibers can be twisted, leading to possible Chiral matrix arrays of certain 3-forms defined as Topological Torsion and Topological Spin. A significant result demonstrates how the coefficients of Affine Torsion are related to the concept of Field excitations (mass and charge); another demonstrates how thermodynamic evolution can describe the emergence of topological defects in the physical vacuum.