  Based on an analysis of the entropy associated to the vacuum quantum
fluctuations, we show that the holographic principle, applied to the cosmic
scale, constitutes a possible explanation for the observed value of the
cosmological constant, theoretically justifying a relation proposed 35 years
ago by Zel'dovich. Furthermore, extending to the total energy density the
conjecture by Chen and Wu, concerning the dependence of the cosmological
constant on the scale factor, we show that the holographic principle may also
lie at the root of the coincidence between the matter density in the universe
and the vacuum energy density.
