Discreteness as ontology: A hodon-based approach to dark matter

TL;DR

The paper investigates a discrete-spacetime hypothesis in which non-material hodons form a statistical substrate for gravity, positing that dark matter phenomenology arises from holographically bounded hodon distributions rather than new particles. By introducing a covariant hodon density $\mathcal{N}(x^{\mu})$ and an entropy-driven evolution equation, the authors derive an emergent stress-energy contribution that yields gravitational clumpiness and halo structures while suppressing small-scale power in line with Lyman-$\alpha$ and weak-lensing constraints. A minimal virial toy model demonstrates how halo cores and flat rotation curves can emerge without particle interactions, and curvature-sensitive scaling explains how hodon properties adapt to local geometry. The framework also differentiates strong and weak holography, integrates Bousso’s covariant entropy bound, and provides a pathway to cosmological phenomenology via a covariant hodon density field. Overall, the hodon model offers a falsifiable, information-geometric alternative to particle dark matter that remains compatible with general relativity and cosmological observations, while inviting empirical tests and further theoretical development.

Abstract

This work proposes a geometric-statistical reinterpretation of the dark sector, grounded in a discrete spacetime framework composed of non-material spatial units termed hodons. Unlike particle-based dark matter models, hodons are kinematically inert and possess ultra-light effective mass derived from vacuum energy density and holographic volume bounds. We introduce a covariant scalar field $\mathcal{N}(x^μ)$ representing local hodon density and derive an entropy-driven evolution equation consistent with causal structure and general relativity. The resulting stress-energy contribution from hodon fluctuations yields gravitational clumpiness without invoking new particles or modified gravity. A virial-based toy model demonstrates that baryonic matter surrounded by hodons forms stable, cored halo profiles, consistent with galactic rotation curves and low-mass halo observations. The framework naturally suppresses small-scale structure via spatial uncertainty relations, aligning with constraints from the Lyman-$α$ forest and weak lensing. By integrating Bousso's covariant entropy bound and distinguishing between strong and weak holography, we situate the model within a broader epistemological context. These results suggest that dark sector phenomenology may emerge from the statistical geometry of space itself, offering a falsifiable alternative to particle dark matter.