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.