Time from Entanglement: A Complete Θ–Field Theory of Gravity, Cosmology, and Black Holes

This manuscript presents a scalar-tensor framework where proper time emerges from quantum entanglement. A dimensionless field Θ encodes entanglement density and couples conformally to matter, reproducing general relativity in the infrared while resolving singularities and providing a mechanism for unitary black hole evaporation. KEY RESULTS • Proven singularity resolution: Collapse bounces at R_b > 0 for M < M_crit = 1/(3√(8πV_0)) • Information recovery mechanism: Explicit 1+1D calculation shows Θ-field correlations restore unitarity • Three testable predictions: - Clock drift: ν̇/ν = Cα²H_0 (detectable in 10 years) - Hawking shift: ΔT/T = -α²/(8π) ≈ -10⁻⁷ - Inflation: r = 12α_I/N² SIGNIFICANCE The work is timely given optical atomic clocks achieving 10⁻¹⁸ stability and upcoming CMB experiments (CMB-S4, LiteBIRD). Unlike other quantum gravity approaches, the theory makes falsifiable near-term predictions. The manuscript provides complete mathematical framework with rigorous derivations, four publication-quality figures, and honest scope statements about ongoing work. SUITABILITY FOR PRD This manuscript addresses core questions in gravitational physics and cosmology with testable predictions, making it ideally suited for Physical Review D's interdisciplinary readership spanning quantum information, general relativity, and precision measurement.