Topological gravity in 3+1D and a possible origin of dark matte

TL;DR

This paper proposes a 3+1D topological gravity framework where Einstein gravity emerges from loop condensation, and uncondensed loops serve as dark matter, predicting unique torsion-related phenomena testable in future experiments.

Contribution

It introduces a super renormalizable topological gravity model in 3+1D that explains dark matter as uncondensed loops and predicts novel torsion effects distinct from standard theories.

Findings

Dark matter modeled as uncondensed loop excitations.

Dark matter sources torsion but not scalar curvature.

Normal matter does not produce torsion in this framework.

Abstract

Dark matter is one of the deepest mystery of the universe. So far there is no natural explanation why the dark matter should exist and even dominate the universe. In this paper, we begin with a 3+1D topological gravity theory which is super renormalizable with vanishing beta functions, then we argue that Einstein gravity can emerge by condensing loop-like excitation from the underlying topological gravity theory. In the meanwhile, the uncondensed loop-like excitations serves as a natural candidate of dark matter and a generalized Einstein equation can be derived in the presence of loop-source(dark matter) background. Surprisingly, we find that such kind of dark matter will not contribute to scalar curvature, however, it will become a source of torsion. Finally, we derive the generalized Einstein equation in the presence of Dirac field. Very different from the usual Einstein-Carton theory, our theory further predicts that any type of normal matter, including Dirac field will not produce torsion. All these unique predictions can be tested by future experiments. Our framework suggests that topological invariant principle might play a more profound role than the well-known general covariance principle, especially towards understanding the nature of dark matter and quantum gravity in 3+1D.