Simple Gravity X: A Scalar Refractive Framework for Gravitational Phenomena

This work presents a comprehensive formulation of the Simple Gravity framework, a scalar theory of gravitation based on an exponential response of local temporal and spatial intervals to a gravitational potential Φ. The framework introduces an effective refractive index n (Φ) = e^-2Φ/c², allowing gravitational effects on light to be described through an optical approach while preserving the local invariance of the speed of light. From this unified structure, the theory consistently derives gravitational redshift, light deflection, and Shapiro time delay, all in agreement with standard weak-field predictions. The dynamics of massive particles is also formulated through an effective action, leading to orbital equations that reproduce perihelion precession in the same regime. A variational formulation of the scalar field is introduced, providing a nonlinear field equation whose weak-field limit recovers the previously used phenomenological form. In addition, an effective covariant structure is developed, enabling comparison with relativistic frameworks while maintaining a non-geometric interpretation of gravity. The theory offers a unified description of gravitational phenomena based on a scalar field and an effective medium, while clearly identifying its current limitations and directions for further development. This work consolidates and extends previous developments in the Simple Gravity series.