We constrain deviations from general relativity (GR) including both redshift and scale dependencies in the modified gravity (MG) parameters. In particular, we employ the under-used binning approach and compare the results to functional forms. We use available datasets such as Cosmic Microwave Background (CMB) from Planck 2018, Baryonic Acoustic Oscillations (BAO) and Redshift Space Distortions (BAO/RSD) from the BOSS DR12, the 6DF Galaxy Survey, the SDSS DR7 Main Galaxy Sample, the correlation of Lyman-$\alpha$ forest absorption and quasars from SDSS-DR14, Supernova Type Ia (SNe) from the Pantheon compilation, and DES Y1 data. Moreover, in order to maximize the constraining power from available datasets, we analyze MG models where we alternatively set some of the MG parameters to their GR values and vary the others. Using functional forms, we find an up to 3.5-$\sigma$ tension with GR in $\Sigma$ (while $\mu$ is fixed) when using Planck+SNe+BAO+RSD; this goes away when lensing data is included, i.e. CMB lensing and DES (CMBL+DES). Using different binning methods, we find that a tension with GR above 2-$\sigma$ in the (high-z, high-k) bin is persistent even when including CMBL+DES to Planck+SNe+BAO+RSD. Also, we find another tension above 2-$\sigma$ in the (low-z, high-k) bin, but that can be reduced with the addition of lensing data. Furthermore, we perform a model comparison using the Deviance Information Criterion statistical tool and find that the MG model ($\mu=1$, $\Sigma$) is weakly favored by the data compared to $\Lambda$CDM, except when DES data is included. Another noteworthy result is that we find that the binning methods do not agree with the widely-used functional parameterization where the MG parameters are proportional to $\Omega_{\text{DE}}(a)$, and this is clearly apparent in the high-z and high-k regime where this parameterization underestimates the deviations from GR.

中文翻译：

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使用红移和尺度分箱对广义相对论偏差的当前限制

我们约束广义相对论 (GR) 的偏差，包括修正重力 (MG) 参数中的红移和尺度依赖性。特别是，我们采用未充分利用的分箱方法并将结果与​​函数形式进行比较。我们使用可用的数据集，例如来自普朗克 2018 年的宇宙微波背景 (CMB)、来自 BOSS DR12 的重子声学振荡 (BAO) 和红移空间失真 (BAO/RSD)、6DF 星系调查、SDSS DR7 主星系样本、相关性来自 SDSS-DR14 的 Lyman-$\alpha$ 森林吸收和类星体、来自万神殿汇编的超新星 Ia 型 (SNe) 以及 DES Y1 数据。此外，为了最大限度地提高可用数据集的约束力，我们分析了 MG 模型，其中我们交替地将一些 MG 参数设置为其 GR 值并改变其他参数。使用函数形式，当使用 Planck+SNe+BAO+RSD 时，我们在 $\Sigma$（而 $\mu$ 是固定的）中发现了高达 3.5-$\sigma$ 与 GR 的张力；当包含透镜数据时，即 CMB 透镜和 DES (CMBL+DES)，这种情况就会消失。使用不同的分箱方法，我们发现，即使将 CMBL+DES 包括到 Planck+SNe+BAO+RSD，在（high-z, high-k）bin 中 GR 高于 2-$\sigma$ 的张力仍然存在。此外，我们在 (low-z, high-k) bin 中发现了 2-$\sigma$ 以上的另一个张力，但是可以通过添加透镜数据来减少这种张力。此外，我们使用 Deviance Information Criterion 统计工具进行模型比较，发现 MG 模型（$\mu=1$, $\Sigma$）与 $\Lambda$CDM 相比，数据较弱，除非 DES数据包括在内。