# On the Vacua of General Relativity in the Backdrop of the Higgs VEV

## TL;DR

This paper explores how augmenting the classical manifold in General Relativity with algebraic structures related to spinor and vector representations leads to the emergence of a Dirac operator and suggests a geometric origin for dark matter linked to the Higgs VEV.

## Contribution

It introduces a novel geometric framework that incorporates algebraic structures to connect the vacuum of General Relativity with dark matter phenomena.

## Key findings

- Emergence of a Dirac operator from the vacuum of General Relativity.
- A volume form with dual character suggests a geometric origin for dark matter.
- Unified vacuum structure potentially explains dark matter as a geometric phenomenon.

## Abstract

The classical notion of manifold may be augmented to institute the algebras associated with the generators of the spinor and vector representations of the Lorentz group on two copies of the cotangent space. In the former case, this results in the emergence of a Dirac operator out of the vacuum of General Relativity. In the backdrop of the Higgs VEV, a volume form with such a dual character endows the augmented manifold with dark matter content as the simplest conceivable geometric structure that could emerge out of the unified vacuum.