A Coherence Field Framework for Galactic Dynamics: From the Λ Scalar Field to the Structural Rigidity of the Radial Acceleration Relation

This work proposes a coherence field framework for galactic dynamics in which the weak gravity regime is governed by a scalar field associated with the structural coherence of spacetime.Within this approach, the empirical Radial Acceleration Relation observed in galaxy rotation curves emerges as a regime dependent modification of the gravitational response. In the quasi static galactic regime the angular structure of the field reduces to an effective radial scalar mode, leading to a modified Poisson equation and an additional gravitational contribution at low accelerations.The resulting dynamics reproduce the characteristic scaling observed in disk galaxies, where the observed gravitational acceleration becomes proportional to the square root of the product between the baryonic acceleration and a characteristic acceleration scale.This characteristic acceleration scale appears to be close to the cosmological acceleration scale associated with the expansion of the universe, suggesting a possible connection between galactic dynamics and large scale properties of spacetime.The framework provides a phenomenological description linking baryonic matter, gravitational potential and a coherence field that modifies the weak gravity regime. The work aims to provide a conceptual and mathematical basis for interpreting galaxy rotation systematics without invoking large quantities of non baryonic dark matter, while remaining compatible with standard gravitational dynamics in the high acceleration regime.