CMG-LCE: Effective Geometric Underdetermination in Gravitational Lensing: A Covariant Coherence-Based Interpretation within Unmodified General Relativity

Effective Geometric Underdetermination in Gravitational Lensing: A Covariant Coherence-Based Interpretation within Unmodified General Relativity Abstract Gravitational lensing is one of the most powerful observational probes of spacetime curvature in the universe. In the standard cosmological interpretation, discrepancies between the observed lensing signal and the amount of visible matter are attributed to dark matter halos surrounding galaxies and clusters. However, gravitational lensing measurements fundamentally constrain spacetime curvature, not the microscopic composition of the stress–energy sources generating that curvature. This work investigates the concept of effective geometric underdetermination in gravitational lensing within the framework of unmodified General Relativity. The central observation is that multiple physical stress–energy configurations may generate indistinguishable lensing signatures. Consequently, lensing observations alone may not uniquely determine the underlying physical origin of the observed curvature. Within this perspective, the paper introduces a covariant effective field theory formulation in which environmental electromagnetic and plasma structures contribute to an additional effective stress–energy component through a coherence-related vacuum response. Importantly, this framework does not modify Einstein’s equations and remains fully consistent with the conservation structure of General Relativity. The model produces falsifiable observational predictions, including a characteristic scaling relation between gravitational lensing convergence and environmental magnetic field strength. These predictions can be tested with forthcoming high-precision surveys such as Euclid, SKA, JWST, and CMB-S4. This study provides the theoretical interpretation of the gravitational lensing analysis presented in CMG-LCE V5.3, and complements previous empirical investigations at galactic and cluster scales (CMG-LCE V5.1 and V5.2). Together, these works form a multiscale observational program exploring whether environmental electromagnetic structure may contribute to gravitational phenomena currently interpreted as dark matter within the geometric framework of General Relativity.