Abstract
We study gravitational baryogenesis in an isotropic and homogeneous universe in the framework of general relativity. We investigate a new exact solution of Einstein's field equations for the FRW metric. Our solution represents a transitioning model of the universe which was expanding in a decelerated mode and passes on to an accelerated mode after dominance of the cosmological constant A. We observe that gravitational baryogenesis occurs in the derived universe, and the derived baryon-entropy ratio is in good agreement with its observational value.