A Generalized Metric for the Average Distribution of Matter ‎on Cosmological Scales: Toward an Alternative ‎Interpretation of Cosmic Flatness?‎

Abstract

Building upon our previous studies, we introduce a generalized metric, denoted G, ‎describing the average gravitational field of a homogeneous universe. Starting from the ‎weak-field approximation of the Schwarzschild metric, the local gravitational contribution ‎of an isolated mass is extended to a continuous cosmological matter distribution, leading ‎to a global gravitational potential proportional to ρ_u R_u^2, where ρ_u is the mean cosmic ‎density and R_u is the Hubble radius. The resulting metric naturally defines an effective ‎cosmological refractive index. For a universe at critical density, this index is found to be ‎exactly 2, while departures from perfect homogeneity may increase it toward approximately ‎‎2.4. We further show that incorporating the gravitational potential of the universe into the ‎metric provides a quantitative framework connecting critical density, Mach’s principle, ‎inertia, and the equivalence of inertial and gravitational mass. Within this approach, ‎cosmic flatness is interpreted as a natural consequence of the global gravitational structure ‎rather than as a property requiring finely tuned initial conditions. The proposed framework ‎offers an alternative perspective on several outstanding problems in cosmology while ‎remaining within the weak-field approximation of general relativity. Its broader ‎cosmological implications, including possible reinterpretations of phenomena commonly ‎attributed to dark matter and dark energy, are discussed cautiously and presented as ‎directions for further investigation.‎