Cosmology from the Scalar Temporal Field: Unifying Dark Matter and Dark Energy via ∇τ Dynamics

This work develops a complete cosmological formulation of the Scalar Temporal Field Ontology (STFO), in which time is a physical scalar τ(x) whose gradient defines causal order and disformally dresses matter geometry. Spatial gradients of τ contribute an effective clustering density ρτ^grad that reproduces dark-matter phenomenology, while the temporal potential V(τ) yields w ≈ −1 and drives cosmic acceleration. The chain matter → radiation → τ closes energy accounting: the apparent “missing mass’’ is τ-content curvature, and dark energy is τ-pressure. We derive modified Friedmann and Poisson equations, discuss rotation curves and lensing in the disformal frame, and outline viability under GW170817 (cT ≈ 1), CMB, DESI, and LSS growth constraints. STFO therefore unifies dark matter and dark energy without new particles, providing falsifiable predictions distinguishable from ΛCDM.