We consider the growth rate of matter perturbations in the Einstein dark energy theory. The theory consists of the Einstein–Hilbert Lagrangian plus the trace of the energy momentum tensor, coupled non-minimally to a dynamical vector field. We will show that the theory has three fixed points corresponding to the dust, radiation and de Sitter universes. Due to the present of trace of the energy–momentum tensor in the Lagrangian, the fixed points occurs in different locations compared to \(\Lambda \)CDM theory. We will analyze the theory with and without cosmological constant. We will fit the model parameters using two independent data sets corresponding to the Hubble parameter H and also \(f\sigma _8\). The theory is then shown to be consistent with observational data.

我们在爱因斯坦暗能量理论中考虑了物质扰动的增长率。该理论包括爱因斯坦–希尔伯特·拉格朗日加上能量动量张量的迹线，该迹线非最小地耦合到动态矢量场。我们将证明该理论具有三个固定点，分别对应于尘埃，辐射和de Sitter宇宙。由于存在拉格朗日能量动量张量的痕迹，因此与\（\ Lambda \） CDM理论相比，固定点出现在不同的位置。我们将分析有或没有宇宙学常数的理论。我们将使用两个独立的数据集拟合模型参数，这些数据集分别对应于哈勃参数H和\（f \ sigma _8 \）。然后表明该理论与观测数据是一致的。