In this manuscript, we have researched the cosmic expansion phenomenon in flat FRW Universe through the interaction of the recently proposed Rènyi holographic dark energy (RHDE). For this reason, we assumed Hubble (H) and Granda–Oliveros (GO) horizons as IR cut-off in the framework of f(R, T) gravity. With this choice for IR cut-off, we can obtain some important cosmological quantities such as the equation of state \(\omega _{T}\), energy density \(\rho _{T}\), density parameter \(\Omega _{T}\), and pressure \(p_{T}\), which are the function of the redshift z. It is observed that in both IR cut-offs the EoS parameter displays quintom-like behaviour for three different values of \(\delta \). Here, we plot these parameters versus redshift z and discuss the consistency of the recent findings. Next, we explore the \(\omega _{T}\)–\(\omega _{T}^{\prime }\) plane and the stability analysis of the dark energy model by a perturbation method. Our findings demonstrate that the Universe is an accelerating model of rapid growth that is explained by quintom like behaviour. Hence, the feasibility of the RHDE model with Hubble and GO cut-off is supported by our model. The results indicate that the IR cut-offs play a significant role in the understanding of the dynamics of the universe.

在这份手稿中，我们通过最近提出的雷尼全息暗能量（RHDE）的相​​互作用研究了平面FRW宇宙中的宇宙膨胀现象。因此，我们将哈勃（H）和格兰达-奥利弗索斯（GO）视界假定为在f（R，  T）引力框架内的IR截止。通过选择红外截止，我们可以获得一些重要的宇宙学量，例如状态方程\（\ omega _ {T} \），能量密度\（\ rho _ {T} \），密度参数\（ \ Omega _ {T} \）和压力\（p_ {T} \），它们是redshift z的函数。可以看出，在两个IR截止中，EoS参数对于\（\ delta \）的三个不同值都显示出类似quintom的行为。在这里，我们绘制了这些参数与红移z的关系图，并讨论了最近发现的一致性。接下来，我们探索\（\ omega _ {T} \） – \（\ omega _ {T} ^ {\ prime} \）平面，并通过扰动方法对暗能量模型进行了稳定性分析。我们的发现表明，宇宙是一种快速增长的加速模型，这一现象可以通过行为学之类的现象来解释。因此，我们的模型支持带有Hubble和GO截止的RHDE模型的可行性。结果表明，IR截止值在了解宇宙动力学方面起着重要作用。