A Time-Curvature Framework Addressing Sixteen Major Tensions in Modern Cosmology

This paper constitutes Trilogy + 1, extending the Time-Curvature Trilogy composed of “Time Curvature as the True Origin of Cosmic Acceleration,” “Time Curvature in FLRW Cosmology: Supernova and Hubble Constraints,” and “Time Curvature Revealed by a Billion Years of Cosmic Evolution.” While the first three papers establish the geometric framework of nonlinear cosmic time and test it against supernova and cosmological evolution data, the present work broadens the analysis to a comprehensive set of major observational tensions in modern cosmology. Within the time-curvature framework—where the mapping between observer time and cosmological evolution time is allowed to be nonlinear while preserving the Einstein field equations and the FLRW metric—multiple longstanding anomalies are revisited under a unified geometric interpretation. The analysis argues that many of these tensions may arise from the implicit assumption of linear cosmic time rather than from missing physical components such as dark energy or modifications of gravity, suggesting that temporal geometry itself may play a central role in resolving several persistent cosmological crises.