Cosmological applications of a geometrical interpretation of "c"

We make the hypothesis that the velocity of light and the expansion of the universe are two aspects of one single concept connecting space and time in the expanding universe. We show that solving Friedman's equations with that interpretation (keeping c = constant) could explain number of unnatural features of the standard cosmology. We thus examine in that light the flatness and the quintessence problems, the problem of the observed uniformity in term of temperature and density of the cosmological background radiation and the small-scale inhomogeneity problem. We finally show that using this interpretation of c leads to reconsider the Hubble diagram of distance moduli and redshifts as obtained from recent observations of type Ia supernovae without having to need an accelerating universe.