Unified Interference Cosmology (UIC): A Unified Field Framework Based on Cosmic Interference and the Hosting Medium

Unified Interference Cosmology (UIC) presents a unified scalar-field framework in which observed gravitational phenomena emerge from perturbations of a hosting cosmic medium identified observationally with the dark-energy sector. The theory introduces a variational formulation based on a single scalar field, derives the corresponding Euler–Lagrange field equation, establishes local conservation laws through Noether symmetry, demonstrates linear stability, recovers the Newtonian weak-field limit, and develops an effective weak-field spacetime correspondence reproducing gravitational redshift, light deflection, and Shapiro time delay. The framework introduces no additional physical fields beyond the scalar perturbation, no free fitting parameters after normalization to Newton's gravitational constant, and explicitly distinguishes mathematical correspondences from fundamental physical derivations. The manuscript concludes with observational predictions, falsification criteria, and a complete mathematical appendix containing the intermediate derivations omitted from the main text. The present work is proposed as a falsifiable theoretical framework whose validity depends on future mathematical development and independent observational testing.