Tensional Geometry Cosmology (TGC): A Curvature-Based Framework for Dark Matter and Dark Energy

Author: C. Duke
Status: Preprint – Submitted to viXra and GreyArray
Date:

Abstract

We propose a new cosmological framework, Tensional Geometry Cosmology (TGC), in which both dark matter and dark energy emerge not from particles or exotic fields, but from the intrinsic tension and curvature of spacetime itself. This model unifies four sub-theories:

  1. Primordial Shell Theory (PST) – Dark matter is the geometric residue of the original singularity’s shell post-expansion.
  2. Curvature-Linked Shadow Geometry (CLSG) – Dark matter is a property of curved spacetime that arises wherever geometry reaches specific configurations.
  3. Curvature-Absence Expansion Hypothesis (CAEH) – Dark energy is the expansive response of spacetime to flatness, not vacuum energy.
  4. Inertial Curvature Hypothesis (ICH) – Curvature can persist and carry inertia independently of mass, explaining lensing anomalies like the Bullet Cluster.

Together, these form TGC: a unified framework where gravity, expansion, and dark matter are all manifestations of a single principle—tension in geometry.

1. Introduction

Current models explain dark matter via unknown particles and dark energy via vacuum pressure. These explanations, while useful for fitting data, remain disconnected, untested, and unsatisfying from a geometric standpoint.

TGC proposes a geometric-first framework: spacetime itself contains zones of tension and relaxation, and these geometries appear as matter or energy to our instruments.

2. Primordial Shell Theory (PST)

PST posits that when the Big Bang occurred, the singularity did not expand evenly. Instead, its "shell"—a kind of geometric residue—was stretched and fractured, embedding curvature into space itself. This leftover structural tension is observed today as the dark matter halo. Unlike particles, it is not localizable; it is the structure of geometry itself.

3. Curvature-Linked Shadow Geometry (CLSG)

CLSG explains that specific spacetime curvature regimes (e.g. deep gravitational wells, galaxy formation zones) exhibit a shadow geometry—extra curvature that cannot be directly observed via electromagnetic interaction, but bends spacetime and affects motion.

This explains the stability of galaxies and lensing effects without requiring WIMPs or other particles.

4. Curvature-Absence Expansion Hypothesis (CAEH)

CAEH posits that expansion occurs not because of energy in space, but because flatness is unstable. Wherever geometry approaches zero curvature (flat), tension forces create expansion.

This explains why dark energy seems uniform—flatness is uniform. And why it accelerates over time—more of space is flattening out.

5. Inertial Curvature Hypothesis (ICH)

To explain persistent lensing in phenomena like the Bullet Cluster, ICH suggests that curvature has inertia—it can retain its shape even after the mass that created it moves.

This allows curved zones (e.g. from a galaxy) to drift and interact like massive objects, even if their matter is displaced. It solves the "dark matter collision offset" paradox.

6. Unified Framework: TGC

Tensional Geometry Cosmology (TGC) brings these together: spacetime is not passive, but an elastic field under tension.

7. Predictions & Testability

TGC predicts that:

Testable via:

8. Conclusion

TGC removes the need for unknown particles or vacuum energy by re-centering gravity as active geometry. It treats spacetime as an elastic, reactive medium where tension shapes evolution.

As data improves and geometric mapping becomes more precise, TGC may offer a simpler, unified understanding of what we now call dark matter and dark energy—not as things, but as curvature with consequence.

9. References & Appendix

[1] To be added upon peer feedback and versioning
[2] Diagrams of curvature shells, expansion fields, and predicted lensing overlays to be included

This document may be cited as:
Duke, C. (2025). Tensional Geometry Cosmology. GreyArray / viXra preprint.

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