We revisit the evolution of the scale factor in a flat FLRW spacetime with a new generalized decay rule for the dynamic $\Lambda$-term under modified theories of gravity. It analyzes certain cosmological parameters and examines their behaviours in this generalized setting which includes several decay laws in the literature. We have also obtained observational constraints on various model parameters and estimated the present values of cosmological parameters $\{{\Omega }_{m_0}$, ${\Omega }_{{\Lambda }_0}$, $q_0,t_0$, ${\omega }_0\}$ and have discussed with various observational results. Finite time past and future singularities in this model are also discussed.

中文翻译：

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具有作为物质和几何函数的动力学 Λ 的平面 FLRW 模型

我们使用新的广义衰减规则重新审视平坦 FLRW 时空中比例因子的演变 $\Lambda$- 修正引力理论下的术语。它分析了某些宇宙学参数并检查了它们在这个广义环境中的行为，其中包括文献中的几个衰变定律。我们还获得了对各种模型参数的观测约束，并估计了宇宙学参数的现值$\{{\Omega }_{{米}_0}$, ${\Omega }_{{\Lambda }_0}$, $q_0,{吨}_0$, ${\omega }_0\}$并与各种观察结果进行了讨论。还讨论了该模型中过去和未来的有限时间奇点。