Probabilistic Presentism: A New Unified Formulation of Time, Gravity, and the Dark Sector

This deposit contains the complete English translation of V2 (2026-01-10) of the preprint “Présentisme probabiliste : nouvelle formulation unifiée du temps, de la gravité et du secteur sombre”. Published French source and version history. Published French V2: Zenodo 18207811 — DOI: 10.5281/zenodo.18207811 Concept DOI for the French work: 10.5281/zenodo.17899327 Previous French version (V1): Zenodo 17899328 — DOI: 10.5281/zenodo.17899328 Core idea. Only the present has ontological existence; the future does not yet exist, but appears as a set of possible futures. This structure is locally encoded by a bounded scalar field π(x) (0 = very open future, 1 = strongly constrained future), endowed with local covariant dynamics. Minimal core (single-field model). The model is formulated as a minimalist field theory in which the dark sector is read directly from the stress-energy tensor of the field π: “Dark matter”: the dynamical component of π's energy (gradients/excitations), denoted ρπdyn. “Dark energy”: the potential contribution V(π), equivalent to an effective cosmological constant (negative pressure). Newtonian bridge. In the static regime, the equation for π leads to a Poisson-type equation and makes it possible to identify an effective potential Φ = Φ0·π whose gradient governs acceleration. Status. Exploratory document (preprint): the objective is readable internal consistency and a minimal covariant framework; explicitly postulated choices (the form of V(π), the reading “dark sector = T(π)μν”, and the statistics of the noise ξ) are identified as such. V2 changelog (very short) Radical simplification: single-field π model (removal of the separate memory field/density). Unified dark sector: decomposition of T(π)μν into a dynamical component (ρπdyn) and a potential component (V(π)). FRW cosmology made “auditable”: explicit equations in terms of ρvis + ρπ. Focused stochasticity: optional scalar noise ξ (short-range correlations). This English edition is a translation, not a revised scientific version. It preserves the equations, notation, references, argumentative structure, limitations, and epistemic qualifications of the published French V2.