P-9: Geometric Candidates for Dark Matter — From 10 GeV Topological Solitons to Cosmic Vortex Bundles

Abstract:The nature of dark matter is one of the most profound mysteries of 21st-century physics. Within the framework of Space Ontology, we propose and rigorously establish a novel dark matter candidate: a topological soliton with mass approximately 10 GeV, which is a "fossil" left over from phase transitions in the early universe. Starting from the spatial orientation field equation and the soliton scaling law, we derive its mass, stability, and annihilation cross-section endogenously. We then demonstrate that its coupling to ordinary matter is naturally suppressed by the gravitational scale, yielding a direct detection cross-section as low as ~10⁻¹⁰⁶ cm², which perfectly explains the null results from the most sensitive direct detection experiments—XENONnT, LZ, and PandaX-4T—with a discrepancy of about 59 orders of magnitude. Finally, we construct a "cosmic vortex bundle" model that connects these microscopic solitons to galactic dark matter halos, revealing the central physical picture that "dark matter is uncondensed spatial vortices," and propose a unique, astronomically testable prediction: a "gamma-ray spatial-energy correlation." We conclude that dark matter is not an unknown particle, but a macroscopic manifestation of the topological structure of space itself. This paper is the ninth in the first series (17 papers total) of Space Ontology, establishing geometric candidates for dark matter from topological solitons to cosmic vortex bundles.