A generalized metric for the average distribution of matter on the cosmological scale: toward a clear and flat universe?

Following on from our previous works on cosmology, we propose a generalized metric, denoted G, applicable to the universe as a whole, treated as homogeneous and filled with matter at its average density. Using the weak-field approximation, the individual Schwarzschild terms M/r are extended to a continuous cosmological medium, yielding a global gravitational potential proportional to ρuRu², where ρu is the mean cosmic density and Ru the Hubble radius. The resulting metric can be interpreted through an effective cosmological refractive index of vacuum. For a critical homogeneous universe, this index is exactly 2. Taking into account large-scale inhomogeneities and the nonlinear dependence of the index on density increases its value, possibly up to about 2.4. As suggested in our previous works, a cosmological light speed reduced by a factor of about 2.4 relative to its local value c0 offers a unified explanation for several phenomena commonly attributed to dark matter and dark energy, etc.. Incorporating the gravitational potential generated by the total mass of the universe into the metric also provides a new perspective on Mach’s principle: inertia appears as a response to the influence of the universe as a whole. The equivalence of inertial and gravitational mass follows naturally in a critical universe, where the global potential is of order c0². In this framework, cosmic flatness emerges from an extended Machian relation rather than from inflation, opening the way to alternative cosmological models without dark matter or dark energy.

Cosmology; Mach’s principle; critical density; gravitational potential; cosmological refractive index