The present study investigates the Friedmann–Lemaitre–Robertson–Walker models (often FLRW models) with time varying G and \(\Lambda \) in the general theory of relativity. In this communication the Einstein field equations have been solved by considering the deceleration parameter q(t) as a varying function of time t and the Hubble parameter H defined as \(q=-l(t-t_0)+\beta -1\) and \(q=-1+\frac{2\alpha (H-1)}{H}\), where \(l,t_0,\beta , \alpha \) are non-negative constants. We have analyzed the values of different constants that will generate a transition for the universe from an early decelerating phase to a recent acceleration phase. The physical and graphic behaviour have also been planned to study in this communication.

本研究研究了广义相对论中具有时变G和\(\Lambda \)的 Friedmann-Lemaitre-Robertson-Walker 模型（通常是 FLRW 模型）。在此通信中，通过将减速参数q ( t ) 视为时间t的变化函数，并将哈勃参数H定义为\(q=-l(t-t_0)+\beta -1\ )和\(q=-1+\frac{2\alpha (H-1)}{H}\)，其中\(l,t_0,\beta , \alpha \)是非负常数。我们分析了不同常数的值，这些常数将导致宇宙从早期减速阶段过渡到最近的加速阶段。物理和图形行为也计划在这次交流中进行研究。