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

TL;DR

This paper introduces a novel dark matter model based on discrete spacetime units called hodons, which generate gravitational effects through their entropy-driven fluctuations without requiring new particles.

Contribution

It presents a geometric-statistical reinterpretation of dark matter using hodons, integrating holography and entropy principles to explain galactic phenomena.

Findings

Hodon fluctuations produce gravitational clumpiness consistent with galaxy rotation curves.

The model naturally suppresses small-scale structures, aligning with Lyman-alpha and lensing data.

Stable, cored halo profiles emerge from the hodon-based framework.

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 $\mathcal{N}(x^\mu)$ 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-$\alpha$ 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.