Topological Stiffness Effect: A Unified Explanation for Dark Matter and Dark Energy

Topological Stiffness Effect: A Unified Explanation for Dark Matter and Dark Energy Abstract: The Λ cold dark matter (ΛCDM) model has achieved great success on cosmological scales, but it faces two core difficulties: the direct non-detection of dark matter particles and the fine-tuning problem of the cosmological constant. Modified Newtonian Dynamics (MOND) can accurately fit galaxy rotation curves, but it cannot be compatible with galaxy cluster observations and cosmic accelerated expansion, and lacks first-principle support. Based on Emergent Topological Cosmology (ETC), this paper proposes the topological stiffness effect: starting from the hierarchical shielding principle and discrete topological ontology, the topological energy-momentum tensor and the unified equation of state w = -(1-s) (where s is the topological saturation ratio) are derived from first principles, which consistently describes the phenomena of dark matter and dark energy within a single framework. Joint fitting of the rotation curves of 175 late-type galaxies from the SPARC database yields the observed value of the topological stiffness strength A = 0.10 ± 0.01, which falls within the ETC theoretical constraint interval 0.08 < A < 0.12 (derived jointly by PSL(2,7) group theory and the holographic entropy bound) and is not a freely adjustable parameter. The model predicts the current dark energy equation of state w0 ≈ -1.01, which is fully consistent with the Planck 2018 result w0 = -1.03 ± 0.03 within the 1σ error range. This paper also presents three quantitatively falsifiable predictions that can be tested by next-generation survey telescopes such as SKA and Euclid. Core Contributions: 1. Derived the topological energy-momentum tensor and unified equation of state w = -(1-s) from first principles, realizing a unified description of dark matter and dark energy across cosmic scales. 2. Jointly fitted 175 galaxy rotation curves from the SPARC database to obtain the topological stiffness strength A = 0.10 ± 0.01, which is locked by ETC theoretical constraints and observational data, with no free parameter tuning. 3. Predicted the present-day dark energy equation of state w0 ≈ -1.01, which is consistent with Planck 2018 observations and avoids the cosmological constant fine-tuning problem. 4. Proposed three quantitatively falsifiable observational predictions that can distinguish this model from ΛCDM and MOND using next-generation telescopes (SKA, Euclid).