Cosmological Update Dynamics: A Probability Field Framework for Cosmological Structure Formation

We propose Cosmological Update Dynamics (CUD), a probabilistic framework in which cosmic evolution is described as the dynamical restructuring of a probability field defined on a statistical manifold. Within this perspective, the universe is represented by a probability density ρ whose evolution follows a drift–diffusion dynamics driven by gradients of a structural instability field φ derived from the log-density variable. The framework introduces probabilistic phase-jump updates that occur when instability thresholds are exceeded, producing discrete restructuring events in the probability landscape. These updates provide a possible mechanism for episodic structure formation in cosmic evolution. The present work formulates a unified dynamical equation combining continuous probability flow and phase-jump processes: ∂tρ = ∇·(D∇ρ − μρ∇φ) + J[ρ, φ]. This paper presents Version 2 of the CUD framework, extending the initial proposal with a formal dynamical structure and exploring its potential implications for cosmological structure formation.