Observational Validation of Time Curvature Using Supernovae, BAO, and CMB Measurements

This paper tests a geometric reinterpretation of cosmic expansion in which cosmic time is allowed to evolve nonlinearly through the mapping τ = t^α while preserving the Einstein field equations and early-universe physics. The framework is confronted with the three primary observational pillars of modern cosmology: Type Ia supernovae from the Pantheon+ dataset, baryon acoustic oscillation measurements from the DESI DR2 distance ladder, and the cosmic microwave background acoustic scale measured by Planck. Because the temporal deformation leaves the sound horizon and recombination physics unchanged, it modifies only the late-time distance–redshift relations through the temporal Jacobian. The analysis shows that all three independent probes converge on the same deformation parameter α ≈ 2.23, indicating that the apparent late-time acceleration of the universe can be interpreted as a geometric consequence of nonlinear cosmic time rather than vacuum energy. This unified constraint provides an observational validation of the time-curvature hypothesis and suggests a new geometric perspective on the cosmological constant problem while maintaining consistency with established cosmological observations.