Spacetime and dark matter from spontaneous breaking of Lorentz symmetry

TL;DR

This paper proposes a model where spontaneous Lorentz symmetry breaking leads to a formulation of gravity involving a connection and scalar field, potentially explaining dark matter as dust within a pre-geometric framework.

Contribution

It introduces a gauge theory of the Lorentz group that naturally incorporates Ashtekar's formulation and suggests a novel link between symmetry breaking and dark matter.

Findings

Gravity described by a Lorentz-valued connection and scalar field.

Spacetime metric emerges only after symmetry breaking.

Potential explanation for dark matter as dust.

Abstract

It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of General Relativity accompanied by dust. From this perspective, gravity is described entirely by a connection $\omega$ valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field $\tau$. The model is "pre-geometric" in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not broken.