Dark Matter as Fractal Solitons: Resolution of the Three Core CDM Problems
Year: 2026
Type: preprint
Abstract: Cold Dark Matter (CDM) particle models face three persistent observational failures at galactic sub-structure scales: the core-cusp problem, the missing satellites problem, and the too-big-to-fail problem. Direct detection experiments (XENON, LUX, PandaX) have found no WIMP signal after four decades of searching. We propose that dark matter consists of fractal solitons β topologically stable, spatially extended wave packets arising from the Fibonacci harmonic cascade of the Fractal Mechanics framework. Unlike point-like WIMPs, fractal solitons span Ξπ β 20β30 cascade levels (βΌ 1β10 kpc physical size), producing flat-core density profiles π(π) = πβ/(1 + (π/π_π)Β²) from quantum pressure, naturally resolving the core-cusp problem. Solitons below πcrit βΌ 106 πβ evaporate via quantum tunneling, reducing the subhalo count from βΌ 500 (CDM prediction) to βΌ 50 (observed), resolving the missing satellites problem. Their extended size makes them susceptible to tidal disruption even at large masses, resolving too-big-to-fail. The effective cross-section for nucleon scattering is π_sol βΌ 10β70 cmΒ², explaining the absence of direct detection signals without fine-tuning. We predict universal soliton-core scaling relations testable with JWST and the Rubin Observatory, and a characteristic gravitational wave signature detectable by LISA.
Author: Leroy, RΓ©mi
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161701684