Cosmological consequences of a time-dependentΛterm

The phenomenological approach to investigate the decay of the effective cosmological constant, as recently proposed by Chen and Wu, is generalized to include a term proportional to $H^2$ on the time dependence of $\Lambda$, where $H$ is the Hubble parameter. This new term can modify some features of the standard Friedmann-Robertson-Walker model and its free parameter may be adjusted in accordance with nucleosynthesis constraints. The model also allows a deceleration parameter $q_0$ assuming negative values so that the density parameter ${\Omega }_0$ is smaller than ⅔ and the age of the Universe is always bigger than $H_0^{-1\mathrm{}}$. In these cases, the usual matter creation rate appearing in models with a decaying vacuum energy is smaller than the one present in the steady-state model.