A Stochastic Interpretation of Dark Energy from Sparse Microscopic Reactions in Cosmic Cauldrons

Standard cosmological models typically invoke a global cosmological constant (Λ) or dynamical scalar fields to explain the accelerated expansion of the universe. In this work, we propose an alternative stochastic-emergent framework in which vacuum-like cosmological behavior arises from microscopic transport processes operating across an overlapping network of local reaction domains. Space is modeled as a statistical fabric composed of discrete “cauldrons” defined at approximately the 1 cm3 scale. These cauldrons are treated as rigid proper volumes whose internal stochastic interactions do not dilute under global cosmic expansion. Instead, the large-scale expansion manifests through the continual emergence and overlap of sparse microscopic domains embedded within an overwhelmingly empty spatial background. Each cauldron contains only a small number of randomly interacting particles, characterized by stochastic decay constants, random collision pathways, and probabilistic energytransfer channels. Energy exchange between overlapping cauldrons generates a transport network whose ensemble-averaged energy density approaches an approximately volumeinvariant steady state. Under this condition, the emergent effective pressure naturally converges toward a vacuum-like equation of state with w ≈ −1. The framework is evaluated through a 100,000-realization Monte Carlo simulation using Latin Hypercube Sampling and tested against the Pantheon+ supernova compilation and Planck PSZ2 cluster catalogue. The resulting expansion histories remain observationally degenerate with standard ΛCDM cosmology across current observational precision. Rather than replacing general relativity or the cosmological constant paradigm, the proposed model offers a possible microscopic statistical interpretation for the emergence of dark-energy-like behavior from sparse stochastic transport processes.