The possibility that the cosmological constant is decaying as the universe grows is explored, and we define a cosmological parameter, depending of the vacuum energy and the universe radius, which should be presently ca. 122 orders of magnitude smaller than at the Planck epoch. From it, a new version of the Friedmann equation for a flat universe is obtained, which allows the estimation of the Hubble parameter at any epoch and the reconstruction of the expansion history. The main result is a quasi-linear expansion dynamics in concurrence with a number of previous works. This behavior is compatible with the main features of observational cosmology and avoids the horizon, flatness, cosmological constant, coincidence and age problems without the need of neither inflation nor initial fine-tuning.