Stratified Density Gravity: Gravitation Without Fundamental Time

Abstract

We present Stratified Density Gravity (SDG), a reformulation of gravitation in which the fundamental manifold is described by (x,y,z,ρ) rather than (t,x,y,z), with ρ representing local gravitational depth / energy density. In this framework time is not a fundamental coordinate; instead, it emerges as a macroscopic ordering parameter associated with irreversible relaxation of density stratification (entropy production). We show that curvature is sourced by spatial stratification of ρ and we obtain a field equation in which local curvature depends on inhomogeneities in ρ, while large-scale curvature depends on the homogeneous background component of ρ. The local sector reproduces Newtonian gravity in the weak-field limit, which fixes the relevant coupling. The global sector yields a dynamical large-scale curvature term that provides an alternative to the cosmological constant Λ and explains cosmic acceleration as a background-density phase. Because curvature depends on second spatial derivatives of ρ, singularities do not form in collapsed regions: high density cores remain finite. The framework therefore preserves the known weak-field and observational successes of General Relativity (GR) while addressing the cosmological constant problem and the classical singularity problem.