Relativity and Cosmology

    

Dark Matter as Cantor Dust: Numerical Evidence

Authors: Ervin Goldfain

As benchmark model of complex dynamics, Stuart-Landau (SL) equation describes the universal behavior of nonlinear oscillators near a Hopf bifurcation. The bifurcation gives birth to a stable, finite-amplitude periodic motion called a limit cycle. Here we develop a one-dimensional toy model showing how Dark Matter (DM) follows from the SL equation. We outline how fluctuations in the control parameter of the SL equation generate progressive amplitude fragmentation, a process mimicking the iterative construction of Cantor sets. The emerging structure freezes in a cosmological phase known as Cantor Dust, a spontaneously broken condensate whose effective dimension flows from D = 1 to a non-integer value D < 1 . The resulting fractal dimension computed numerically reinforces the hypothesis of running spacetime dimensions near the Planck scale.

Comments: 26 Pages.

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Submission history

[v1] 2025-12-12 20:59:34
[v2] 2025-12-18 13:57:30

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