In this paper, we study a particular modified gravity Equation of State (EoS), the so-called Jaime–Jaber–Escamilla, that emerges from the first gravity modified action principle and can reproduce three cosmological viable f(R) theories: the Starobinsky, Hu–Sawicki and Exponential models. This EoS is a suitable candidate to reproduce the dynamical dark energy behaviour already reconstructed by the current data sets. Based on the joint statistical analysis, we found that our results are still in good agreement (within 1σ) with the ΛCDM, while at perturbative level, we note that the matter power spectrum normalisation factor σ8 shows an agreement with SDSS and SNeIa+IRAS at 1-σ for the Starobinsky model and with SDSS-vec for the Hu–Sawicki and Exponential models. Furthermore, we found that for the H0 values, Starobinsky and Hu–Sawicki show the least tension in comparison with PL18 TT. All these aspects cannot be observed directly from other alternatives theories, where an equation of state is difficult to compute analytically.

中文翻译：

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受修正重力启发的动态暗能量的线性扰动谱

在本文中，我们研究了一种特殊的修正重力状态方程 (EoS)，即所谓的 Jaime-Jaber-Escamilla，它源于第一个重力修正作用原理，可以重现三个宇宙学可行F(R)理论：Starobinsky、Hu-Sawicki 和指数模型。该 EoS 是再现已由当前数据集重建的动态暗能量行为的合适候选者。基于联合统计分析，我们发现我们的结果仍然很好地吻合（在1σ) 与ΛCDM，在微扰水平上，我们注意到物质功率谱归一化因子σ8显示与 SDSS 和 SNeIa+IRAS 在 1-σ用于 Starobinsky 模型，SDSS-vec 用于 Hu-Sawicki 和指数模型。此外，我们发现对于H0与 PL18 TT 相比，Starobinsky 和 ​​Hu-Sawicki 的张力最小。所有这些方面都无法观察到直接地来自其他替代理论，其中状态方程难以解析计算。