The standard cosmological model (ΛCDM) has achieved remarkable success in explaining large-scale structure but relies on two undetected components—dark matter and dark energy—to close the energy budget of the universe. This paper presents the Unified Time Density Theory (UTDT), a comprehensive alternative framework that explains galactic and cosmic dynamics through a modification of the spacetime metric rather than the addition of invisible matter. The theory posits that mass generates a dimensionless time density field Ψ, representing the relative flow rate of time, which manifests physically as an acceleration field a = −c²∇Ψ. We address previous theoretical inconsistencies in scalar field gravity models by: (1) establishing a hierarchical field structure with rigorous dimensional consistency, (2) deriving the characteristic length scale λ = 1.4Rd from first-principles tidal force equilibrium, and (3) correcting the connection to General Relativity through the metric perturbation g₀₀ = 1 + 2Ψ. The theory successfully reproduces galaxy rotation curves for 150 galaxies in the SPARC database (R² = 0.932), resolves the Mass Discrepancy-Acceleration Relation (MDAR), and explains the Bullet Cluster separation via field propagation delays. Furthermore, at cosmological scales, the theory produces an emergent effective cosmological constant that matches observed cosmic acceleration.
Ribeiro, José (2025) studied this question.