Abstract
We have considered a cosmological model with a phenomenological model for the cosmological constant of the form \(\Lambda=\bt\fr{\ddot R}{R}\), \( \bt\) is a constant. For age parameter consistent with observational data the Universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the Universe is \(H_0^{-1}\), where \(H_0\) is the present Hubble constant. The cosmological constant is found to decrease as \(t^{-2}\). Allowing the gravitational constant to change with time leads to an ever increasing gravitational constant at the present epoch. In the presence of a viscous fluid this decay law for \(\Lambda\) is equivalent to the one with \(\Lambda=3\alpha H^2\) (\(\alpha=\rm const.\)) provided \(\alpha=\fr{\bt}{3(\bt-2)}\). The inflationary solution obtained from this model is that of the de-Sitter type.