We have considered a cosmological model with a cosmological constant of the form $\Lambda=3\alpha\frac{ \dot R^2}{ R^2}+\bt\frac{ \ddot R}{ R} \alpha, \bt=\rm const.$ The cosmological constant is found to decrease as $t^{ -2}$ and the rate of particle creation is smaller than the Steady State value. We have found that this behavior gives $\frac{ \Lambda_{ Pl}}{ \Lambda_p}=10^{ 120}$ where $\Lambda_{ Pl}$ is the value of $\Lambda$ at Planck time. Solutions with $\bt=3\alpha$ in the radiation dominated era and $\bt=6\alpha$ in the matter dominated era are equivalent to the FRW results. We have found an inflationary solution of the de-Sitter type with $\bt=3-3\alpha$. Some problems of the Standard Model may be resolved with the presence of the above cosmological constant in the Einstein's equation. Since observations suggest a contribution of the vacuum energy density in the range $0.40<\Omega^\Lambda<0.76$, one gets $4<\beta<12$. If $\alpha=0$ the minimum age of the universe is found to be $H_p^{ -1}$ ($H_p$ is the present Hubble constant) with $\beta=\infty$.
Categories: gr-qc