Scale-relativistic cosmology

The principle of relativity, when it is applied to scale transformations, leads to the suggestion of a generalization of fundamental dilations laws. These new special scale-relativistic resolution transformations involve log-Lorentz factors and lead to the occurrence of a minimal and of a maximal length-scale in nature, which are invariant under dilations. The minimal length-scale, that replaces the zero from the viewpoint of its physical properties, is identified with the Planck length lP, and the maximal scale, that replaces infinity, is identified with the cosmic scale , where Λ is the cosmological constant. The new interpretation of the Planck scale has several implications for the structure and history of the early Universe: we consider the questions of the origin, of the status of physical laws at very early times, of the horizon/causality problem and of fluctuations at recombination epoch. The new interpretation of the cosmic scale has consequences for our knowledge of the present universe, concerning in particular Mach’s principle, the large number coincidence, the problem of the vacuum energy density, the nature and the value of the cosmological constant. The value (theoretically predicted ten years ago) of the scaled cosmological constant ΩΛ=0.75±0.15 is now supported by several different experiments (Hubble diagram of Supernovae, Boomerang measurements, gravitational lensing by clusters of galaxies). The scale-relativity framework also allows one to suggest a solution to the missing mass problem, and to make theoretical predictions of fundamental energy scales, thanks to the interpretation of new structures in scale space: fractal/classical transitions as Compton lengths, mass–coupling relations and critical value 4π2 of inverse couplings. Among them, we find a structure at 3.27±0.26×1020 eV, which agrees closely with the observed highest energy cosmic rays at 3.2±0.9×1020 eV, and another at 5.3×10−3 eV, which corresponds to the typical neutrino mass needed to explain solar neutrino oscillations.