Transit universe with time varying $G$ and decaying $Λ$

We present the model of transit universe from early deceleration phase to current acceleration phase under the framework of general relativity in presence of gravitational coupling $G(t)$ and cosmological terms $Λ(t)$. The Einstein's field equations have been solved by considering time dependent deceleration parameter (DP) which renders the scale factor $a = (t^{n}e^{kt})^{\frac{1}{m}}$ where $m$, $n$ and $k$ are positive constants. The cosmological term $(Λ(t))$ is found to be positive and a decreasing function of time which supports the result obtained from supernovae Ia observations. The geometrical and kinematical features of the model are examined in detail.

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