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Fractal Spatio-temporal Gravity (fsg)

Year: 2025
Type: preprint
Abstract: FRACTAL SPATIO-TEMPORAL GRAVITY (FSG) Abstract We propose a modified theory of gravity based on a Fractal and Non-Local Spacetime Geometry (FSG), obtained from an effective action containing the fractional non-local operator X = □⁻¹R. The effective action induces infrared corrections to General Relativity driven by a dimensional flow. We show that this specific fractional structure implies a reduction of effective spectral dimension towards d_S ≈ 2 in the IR. This geometric reduction is the rigorous cause of the transition to a modified propagator G(k) ∼ k⁻³, which is the requisite condition for MOND dynamics. This leads to: Flat galactic rotation curves without dark matter. An exact baryonic Tully–Fisher relation V⁴ = GM a₀, derived analytically. A natural emergence of the acceleration scale a₀ ≈ c²√(Λ/3). To ensure consistency with Solar System tests, we explicitly derive a source-dependent screening mechanism and compute the PPN parameters, demonstrating convergence to General Relativity at small scales. Regarding cluster dynamics, we demonstrate via 1D conceptual simulation that non-local wave dynamics possess the intrinsic capacity for ballistic overshoot. This offers a qualitative mechanism for the Bullet Cluster phenomenology (separation of mass and potential) driven by the inertia of the vacuum, without requiring collisionless Dark Matter. Cosmologically, the model proposes a "Fractal Boost" mechanism to replace Cold Dark Matter. Preliminary numerical integration of the linear perturbation equations confirms that this geometric enhancement can sustain the acoustic oscillations amplitude during recombination. Additionally, the model predicts a phantom-like equation of state (w₀ < -1), measurable deviations in H(z), and early structure formation consistent with JWST. The theory is fully falsifiable via precision measurements from Euclid.
Author: MARIE-LOUISE, Laurent
Language: English
Open Access status: green
OpenAlex ID: W7108469831
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