Fractal Universe versus Cosmological Principle

Abstract

The homogeneity of the standard relativistic Friedmann (FRW) models, based on the Cosmological principle(CP), is a non-observable spatial geometrical feature of the 3-dim spatial hypersurfaces at any constant cosmic time, where they have a homogeneous local matter density. However, here and now, we can only observe the collected spherical boundaries of the past light cone at different cosmological times, i.e. the sky or observable universe. Hence, the smoothness problem of the observable universe requires to choose a definition of distance to define an averaged density along the past null cone. The surprise is that average densities along the past light cone, constructed from the three observational distances (observer area, luminosity and redshift), may be affected by relativistic effects. Choosing the average densities constructed from the last two observational distances, even the flat Einstein-de Sitter model is observationally inhomogeneous at low redshift values, with some fractal features. An observable fractal universe can be made compatible with standard FRW models, based on the CP, but also with spatially inhomogeneous models (non based on the CP). As a conclusion we finish with the following proposition: “If the Universe looks homogeneous for astronomers, then this is an observational evidence against Friedmann models”.