Decelerating to accelerating FRW universe with variable G and Λ in conharmonically flat space

General exact solutions of the Einstein's field equations by using conharmonically flat space with variable gravitational and cosmological “constants” for a spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with perfect fluid has been obtained. To study the transit behaviour of Universe, we consider a law of variation of scale factor a(t)=(tket)1n which yields a time-dependent deceleration parameter (DP) q=−1+nk(k+t)2, comprising a class of models that depicts a transition of the universe from the early decelerated phase to the recent accelerating phase. We find that the time-dependent DP is reasonable for the present day Universe and give an appropriate description of the evolution of the universe. For n=0.27k, we obtain q0=−0.73 which is similar to observed value of DP at present epoch. It is also observed that for n ≥ 2 and k=1, we obtain a class of transit models of the universe from early decelerating to present accelerating phase. For k=0, the universe has non-singular origin. In these models, we arrive at the decision that, from the structure of the field equations, the behaviour of Λ and G are related. Taking into consideration the observational data, we conclude that the Λ behaves as a positive decreasing function of time whereas G is increasing and tend to a constant value at the late time. Our derived model is in good agreement with ΛCDM model. Some physical and geometric properties of the models are also discussed.