# Fundamental Theory of Torsion Gravity

## TL;DR

This paper develops a comprehensive differential geometry framework for torsion and curvature in spacetime, explores torsion as a massive axial-vector field, and applies it to fundamental problems in gravity, particle physics, and cosmology.

## Contribution

It introduces a unified geometric approach to torsion and curvature, modeling torsion as a Proca field and applying this to address key issues in gravity and particle physics.

## Key findings

- Torsion acts as an axial-vector massive Proca field.
- Torsion stabilizes spinor configurations and influences singularity formation.
- The framework offers new insights into energy positivity and standard model problems.

## Abstract

In this work we present the general differential geometry of a background in which the space-time has both torsion and curvature with internal symmetries being described by gauge fields, and that is equipped to couple spinorial matter fields having spin and energy as well as gauge currents: torsion will turn out to be equivalent to an axial-vector massive Proca field and because the spinor can be decomposed in its two chiral projections, torsion can be thought as the mediator that keeps spinors in stable configurations; we will justify this claim by studying some limiting situations. We will then proceed with a second chapter, where the material presented in the first chapter will be applied to specific systems in order to solve problems that seems to affect theories without torsion: hence the problem of gravitational singularity formation and positivity of the energy are the most important, and they will also lead the way for a discussion about the Pauli exclusion principle and the concept of macroscopic approximation. In a third and final chapter we are going to investigate in the light of torsion dynamics some of the open problems in the standard models of particles and cosmology which would not be easily solvable otherwise.