L.R.S. Bianchi type II Stiff Fluid cosmological model with Decaying Vacuum Energy Density $\mathrm{\Lambda }$ in general relativity

Locally rotationally symmetric (L.R.S.) Bianchi type II stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have assumed a condition $A=B^m$ between metric potentials $A,B$ where $n$ is the constant. It is shown that the vacuum energy density $\mathrm{\Lambda }$ is positive and proportional to $\frac{1}{t^2}$. The values of deceleration parameter $q$, matter-energy density ${\mathrm{\Omega }}_m$ and dark-energy density ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ are found to be in good agreement with the values obtain from 5-years WMAP observations. the predicted value of the jerk parameter agrees with the SNLS SNIa and X-ray galaxy cluster distance data but does not with the SNIa gold sample data. In general, the model represent accelerating, shearing and non-rotating universe.The physical and geometrical behavior of these models are also discussed.