The Universal Twist: Torsion From Graphene to Galaxies

What if the missing pieces of our universe—the dark matter that binds galaxies and the dark energy that drives them apart—are not invisible particles, but a fundamental twist in the fabric of space itself? For over a century, Einstein’s General Relativity has described the universe as a smooth, curved surface.

A comprehensive theoretical synthesis by physicists Nick E. Mavromatos, Pablo Pais, and Alfredo Iorio suggests that curvature has a silent partner: spacetime torsion. While standard gravity ignores this "twist," the team argues it is a mathematical necessity whenever fermions (the building blocks of matter) are present.

Bridging the Gap with the "Geometric Dark Sector"

This discovery matters because it bridges the gap between the unimaginably large and the microscopic. By treating torsion as a dynamical force rather than a geometric footnote, we may finally explain the "Geometric Dark Sector."

It provides a single origin for cosmic inflation and the mysterious energy densities of the vacuum without needing to invent "placeholder" particles.

Core Principles of Spacetime Torsion

A Universal Force Across Scales

The study tracks torsion across 30 orders of magnitude. At the smallest scales, the researchers found that torsion behaves as a universal repulsive four-fermion contact interaction.

This constant repulsion prevents matter from collapsing into infinite densities, potentially solving the "singularity" problem at the heart of black holes.

From Abstract Math to "Tabletop" Experiments

In materials science, this abstract math becomes tangible. In Dirac materials like graphene, physical defects—specifically screw and edge dislocations—map directly onto torsion components.

In these 2D honeycombs, a torsion field acts as an effective mass term. This means we can simulate the physics of the early universe by manipulating the imperfections in a sheet of carbon.

A Driver of Cosmic Evolution

On a cosmological scale, the implications are profound. The study links string-inspired torsion to a "Running Vacuum Model" (RVM), where the energy density is proportional to the fourth power of the Hubble scale ( $\rho_{total} \propto H^4$ ).

This could explain how the universe underwent rapid inflation without requiring a separate "inflaton" field, as the torsion itself drives the expansion.

Open Questions & Future Research

However, the team remains cautious. While the math is elegant, several challenges remain:

Experimental Observation: Direct detection of torsion in gravitational waves is still pending.
Parameter Ambiguity: The "Barbero-Immirzi constant" introduces a key uncertainty.
The Scale Bridge: The transition between emergent torsion in graphene and fundamental cosmic torsion is currently an analogy lacking a direct experimental link.

The researchers conclude that torsion is not optional; it is required for local supersymmetry to hold. As we look toward the next generation of sensors, the hunt for this "universal twist" may be the key to unlocking the dark side of the cosmos.

Reference: Summary based on: "Torsion at different scales: from materials to the Universe" by Nick E. Mavromatos, Pablo Pais, and Alfredo Iorio. Preprints 2022, 2023. (Version: arXiv:2310.13150v3).