In this paper, we study the Rényi holographic dark energy (HDE) model in the context of the Chern–Simons (CS) model of modified gravity theory. Different cosmological parameters, such as energy density, deceleration parameter, equation of state, square of sound speed and cosmological plane, are discussed using the Friedmann–Lemaître–Robertson–Walker spacetime background. Two separate solutions of CS field equations arise. The Rényi HDE model shows the transition from deceleration to acceleration phase which is fully consistent with the observational data while the second case represents a decelerated phase of expansion only. Our results, based on the results of the equation of state obtained, predict that the universe is under the influence of dark energy, and therefore, in an accelerated expansion phase. On the other hand, the second-case solution shows the influence of ΛCDM. In both cases, ω < 0,ω′ < 0 indicated that the Rényi HDE model is in the freezing region and cosmic expansion is more accelerating in the context of CS modified gravity. It is also observed that the value of the squared sound speed, cs2, is positive ∀z ∈ℛ, a sufficient condition for the stability of the system. Hence, it is concluded that the Rényi HDE model is supported by the results of general relativity in the framework of CS modified gravity.

中文翻译：

---

Chern-Simons 引力中的 Rényi 全息暗能量模型：一些宇宙学意义

在本文中，我们在修正重力理论的 Chern-Simons (CS) 模型的背景下研究了 Rényi 全息暗能量 (HDE) 模型。使用弗里德曼-勒梅特-罗伯逊-沃克时空背景讨论了不同的宇宙学参数，例如能量密度、减速参数、状态方程、声速平方和宇宙学平面。CS场方程有两个独立的解。Rényi HDE 模型显示了从减速阶段到加速阶段的过渡，这与观测数据完全一致，而第二种情况仅代表扩张的减速阶段。我们的结果，基于获得的状态方程的结果，预测宇宙受到暗能量的影响，因此处于加速膨胀阶段。另一方面，Λ清洁发展机制。在这两种情况下，ω < 0,ω' < 0表明 Rényi HDE 模型处于冰冻区域，在 CS 修正重力的背景下，宇宙膨胀更加加速。还观察到平方声速的值，Cs2, 为正∀z ∈ℛ，是系统稳定的充分条件。因此，可以得出结论，Rényi HDE 模型得到了广义相对论在 CS 修正重力框架下的结果的支持。