We consider the holographic Friedman–Robertson–Walker (hFRW) universe on the 4-dimensional membrane embedded in the 5-dimensional bulk spacetime and fit the parameters with the observational data. In order to fully account for the phenomenology of this scenario, we consider the models with the brane cosmological constant and the negative bulk cosmological constant. The contribution from the bulk is represented as the holographic dark fluid on the membrane. We derive the universal modified Friedmann equation by including all of these effects in both braneworld and holographic cutoff approaches. For three specific models, namely, the pure hFRW model, the one with the brane cosmological constant, and the one with the negative bulk cosmological constant, we compare the model predictions with the observations. The parameters in the considered hFRW models are constrained with observational data. In particular, it is shown that the model with the brane cosmological constant can fit data as well as the standard $\Lambda$CDM universe. We also find that the ${\sigma }_8$ tension observed in different large-structure experiments can be effectively relaxed in this holographic scenario.

我们考虑嵌入 5 维体时空的 4 维膜上的全息弗里德曼-罗伯逊-沃克 (hFRW) 宇宙，并将参数与观测数据拟合。为了充分考虑这种情况的现象学，我们考虑具有膜宇宙学常数和负体积宇宙学常数的模型。来自体的贡献被表示为膜上的全息暗流体。我们通过在膜世界和全息截止方法中包含所有这些效应来推导出通用的修正弗里德曼方程。对于三种特定模型，即纯 hFRW 模型、具有膜宇宙学常数的模型和具有负体积宇宙学常数的模型，我们将模型预测与观测值进行比较。所考虑的 hFRW 模型中的参数受观测数据的约束。特别是，表明具有膜宇宙学常数的模型可以拟合数据以及标准$\Lambda$CDM 世界。我们还发现，${\sigma }_8$ 在这种全息场景中，可以有效地放松在不同大型结构实验中观察到的张力。