The cosmological constant and the coincidence problem in a new cosmological interpretation of the universal constant c

In a recent paper (Vigoureux et al. Int. J. Theor. Phys. 47:928, 2007) it has been suggested 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. It has then be shown that solving Friedmann's equations with that interpretation (and keeping c = constant) can explain number of unnatural features of the standard cosmology (for example: the flatness problem, the problem of the observed uniformity in term of temperature and density of the cosmological background radiation, the small-scale inhomogeneity problem...) and 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. In the present work we examine the problem of the cosmological constant. We show that our model can exactly generate $\Lambda$ (equation of state $P_\varphi = - \rho_\varphi c^2$ with $\Lambda \propto R^{-2}$) contrarily to the standard model which cannot generate it exactly. We also show how it can solve the so-called cosmic coincidence problem.