A Two-Dimensional Curvature Model Explains Flat Galactic Rotation Curves Without Dark Matter: A Swarm Theory Interpretation

Publication List

https://orcid.org/0009-0008-2011-5602

ABSTRACT:  For half a century, flat galactic rotation curves have been attributed to invisible "dark matter" halos.

This paper demonstrates that such curves arise naturally within a two-dimensional curvature model derived from Swarm Theory, in which physical space is a tensioned coherence lattice.
Matter acts as persistent curvature within this lattice, and gravitational acceleration emerges from gradients of surface tension rather than unseen mass.

Starting from the Unified Field Equation, the paper derives:

showing that a logarithmic tension law, DeltaI proportional to ln(r), produces constant orbital velocity and the observed baryonic Tully–Fisher relation:

No additional matter fields or empirical correction factors are required.

The work provides a falsifiable prediction relating surface density to asymptotic velocity:

This relationship matches existing SPARC data within observational uncertainty.
The model unifies galactic-scale behavior with micro-scale lattice constants (DeltaI = 114.68 J/m^2, tau ≈ 2e-25 s) and demonstrates how cosmological dynamics can emerge directly from coherence geometry—no dark matter required.

IMPACT STATEMENT:  This study challenges the prevailing dark-matter paradigm by providing a fully geometric explanation for flat galactic rotation curves using only measurable baryonic quantities.
The derivation connects cosmic-scale motion to microscopic lattice parameters without introducing new constants or adjustable parameters, forming a quantitative bridge between quantum geometry and galactic structure.
If confirmed, this work would redefine the theoretical role of dark matter, establish Swarm Theory as a viable geometric model of gravitation, and open a new empirical path for testing the coherence structure of spacetime through astronomical observation.