Tensional Geometry Cosmology (TGC)
Cosmic Geometry Series | Published:Disclaimer:
The ideas presented in this document constitute a novel theoretical framework intended to stimulate discussion, investigation, and observational testing. These concepts have not yet been experimentally verified or peer-reviewed. Readers should approach this theory as exploratory cosmological hypotheses rather than established scientific fact.
Tensional Geometry Cosmology (TGC) is a unified theoretical framework proposing that the true architecture of the universe arises not from matter, but from the geometric tension of spacetime itself. Through five interlocking hypotheses, TGC redefines dark matter, dark energy, and cosmic structure as manifestations of pure curvature.
1. The Primordial Shell Theory (PST)
The Big Bang was not a point of mass-energy density but a compact, pre-structured shell of spacetime under extreme geometric tension. This tension was released in a cascading rupture, sending curvature waves outward. These shaped the early cosmic web and seeded the earliest gravitational scaffolds.
“The universe did not begin in heat—it began in shape.”
Curvature density function (initial form):
2. Curvature-Linked Shadow Geometry (CLSG)
Dark matter is not particulate. It is a property of spacetime curvature. When the Ricci curvature tensor exceeds a local threshold, it produces gravitational lensing and rotational anomalies normally attributed to matter.
Curvature mass equivalence approximation:
This explains halo structures, galaxy rotation curves, and dark matter lensing with no need for WIMPs or axions.
3. Edge Geometry Acceleration (EGA)
As the universe expands, its edge regions flatten. This boundary-level relaxation leads to a decrease in curvature tension and manifests as accelerated expansion. Dark energy is not a force—it is a oundary condition.
Expansion linked to curvature gradient:
4. Inertial Curvature Hypothesis (ICH)
Curvature is not instantaneous. Like matter, it has inertia. Regions of high tension resist change and maintain their shape across time—even when the mass that shaped them is displaced. This explains observations such as the Bullet Cluster.
Curvature momentum term:
5. Curvature Arch Hypothesis (CAH)
Why do dark matter halos persist for billions of years? Because curvature arches reinforce themselves. Much like architectural domes, spacetime geometry can create stable, self-supporting regions of gravitational potential.
“Dark matter is not scaffolding—it is structure.”
6. Matter Emergence as Curvature Condensation
In TGC, the 5% of matter we observe is the cooled, condensed end state of extreme curvature. Most of the universe is still geometric structure—just uncondensed. This explains why dark matter and energy dominate the energy budget without visible mass.
Condensation threshold function:
How to Test TGC
- Lensing Without Mass: Identify curvature fields via gravitational lensing where no baryonic mass is present.
- Void Edge Dynamics: Measure anomalous acceleration at the edges of large voids.
- Curvature-Only Halos: Detect persistent lensing zones lacking galaxies.
- Gravitational Wave Aftermaths: Observe curvature inertia effects post-merger.
- Geometry-Based Simulations: Use pure-tension field models to simulate filament networks and halo formation.
Why TGC Matters
This theory turns the universe into a living field of geometry. Mass is no longer fundamental—it is the fossilization of stress. Gravity is not attraction—it is curvature tension. Dark matter is not a missing ingredient—it is an overlooked property of shape.
“If matter is music, then geometry is the instrument.”