We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than 10% and 5% with respect to the $\Lambda$CDM PS at $k\sim 0.01h∕\text{Mpc}$, the parameters have to be in the range $-0.30<g_0<0.32$, $0\le c_g^2<0.01$ and $-0.15<g_0<0.16$, $0\le c_g^2<0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $\Lambda$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles.

我们研究了暗能量（DE）各向异性应力对物质功率谱（PS）特征的影响。我们采用参数化后弗里德曼式（PPF）形式主义来模拟有效的DE，并通过控制其总振幅的两参数方程式对其各向异性应力特性进行建模（$G_0$）和过渡比例（$C_G$）。对于背景宇宙学，我们考虑用不同的状态方程来模拟DE，包括一个常数$w_0$参数，以及提供解冻（CPL）和冻结（nCPL）行为的模型。我们首先使用万神殿，BAO，$H_0$和CMB普朗克数据。然后，我们分析了这些参数在线性PS中的作用。为了使各向异性应力不会引起相对于材料的大于10％和5％的偏差$\Lambda$CDM PS位于 $ķ〜0。01H∕\text{Mpc}$，参数必须在范围内 $-0。30<G_0<0。32$， $0\le C_G^2<0。01$ 和 $-0。15<G_0<0。16$， $0\le C_G^2<0。01$， 分别。此外，我们使用标准扰动理论在实空间和红移空间中计算对PS的领先非线性校正，这表明相对于$\Lambda$CDM得到了增强，尤其是对于四极和十六极RSD多极。