In this work, we construct an interacting model of the Rényi holographic dark energy in the Brans-Dicke theory of gravity using Rényi entropy in a spatially flat Friedmann-Lemaître-Robertson-Walker Universe considering the infrared cut-off as the Hubble horizon. In this setup, we then study the evolutionary history of some important cosmological parameters, in particular, deceleration parameter, Hubble parameter, equation of state parameter, and Rényi holographic dark energy density parameter in both nonflat Universe and flat Universe scenarios and also observe satisfactory behaviors of these parameters in the model. We find that during the evolution, the present model can give rise to a late-time accelerated expansion phase for the Universe preceded by a decelerated expansion phase for both flat and nonflat cases. Moreover, we obtain as , which indicates that this model behaves like the cosmological constant at the future. The stability analysis for the distinct estimations of the Rényi parameter and coupling coefficient has been analyzed. The results indicate that the model is stable at the late time.

中文翻译：

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Brans-Dicke理论中的Rényi全息暗能量相互作用

在这项工作中，我们在空间平的Friedmann-Lemaître-Robertson-Walker宇宙中使用Rényi熵，在Brans-Dicke重力理论中构造了Rényi全息暗能量的相互作用模型，该模型考虑了红外截止作为哈勃视界。在此设置中，我们接着研究了一些重要的宇宙学参数的演化历史，特别是在非平坦宇宙和平坦宇宙场景中的减速参数，哈勃参数，状态方程和Rényi全息暗能量密度参数，并观察了令人满意的行为。这些参数在模型中。我们发现，在演化过程中，本模型可以导致宇宙的后期加速扩展阶段，然后在平坦和非平坦情况下都出现减速的扩展阶段。此外，我们获得 作为 ，表明此模型的行为类似于将来的宇宙学常数。分析了Rényi参数和耦合系数的不同估计的稳定性分析。结果表明该模型在后期很稳定。