Dark energy models with a time-dependent gravitational constant

Two phenomenological models of Lambda, viz. Lambda similar to ((a) over dot/a)(2) and Lambda similar to a/a, are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time, as suggested earlier by others, including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that the Lambda similar to a/a model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model, Lambda similar to ((a) over dot/a)(2), is in general attractive in nature. Moreover, it is seen that due to the combined effect of time-variable. and G the Universe evolved with acceleration as well as deceleration. Deceleration indicates a big crunch.