The Curvature Arch Hypothesis: How Dark Matter May Stabilize Itself

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.

One of the deepest puzzles in physics is how dark matter appears to form stable, long-lasting structures like halos around galaxies — despite not interacting with light or electromagnetic forces. The Curvature Arch Hypothesis (CAH) offers an elegant geometric explanation: dark matter not only arises from curved spacetime, it helps maintain that curvature.

Dark Matter as Structure, Not Substance

In Tensional Geometry Cosmology (TGC), dark matter is not a particle, but a property of spacetime curvature — as proposed in the Curvature-Linked Shadow Geometry (CLSG) model. CAH builds on this by suggesting that this curvature is self-reinforcing — like an architectural arch.

“Dark matter is not held in place by gravity. It is gravity, held in place by shape.”

The Arch Analogy

In architecture, an arch distributes forces in such a way that its own shape holds it together. The more you press down on it, the stronger it becomes — because tension and compression are in perfect balance.

CAH proposes that:

• Curved regions of spacetime act like tension-bearing arches.
• The “dark matter effect” is the feedback loop of geometry maintaining itself under stress.
• This explains the longevity of dark halos — they are self-supporting geometric configurations.

Self-Stabilizing Geometry

This idea explains why dark matter structures persist for billions of years:

• They do not need to be “made of something.”
• They are standing curvature waves — geometric forms locked into place by their own shape.
• They behave like architectural forms in a dynamic field — adapting and resisting collapse via form alone.

Why It Matters

CAH resolves one of the greatest paradoxes in cosmology: how something with no charge, no friction, and no direct interaction with visible matter can still hold galaxies together.

If dark matter is just geometry, and that geometry is inherently self-stabilizing, then the mystery is not how it stays in place — but why it ever moves at all.

Implications and Predictions

• Galactic halos may exhibit resistance to distortion similar to architectural structures under load.
• Gravitational lensing patterns may reflect arch-like stress distributions.
• Simulations of geometry-only models may reproduce halo behavior without particles.

A Universe Built Like a Cathedral

In CAH, the cosmos is not a chaotic explosion of matter, but a precision-tension structure. Galaxies are not floating in a dark fog — they are suspended in arches of pure curvature.

And if this is true, we may come to see the universe not just as expanding… but as designed by its own geometry to hold itself together.