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Current constraints on deviations from General Relativity using binning in redshift and scale

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-$α$ 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-$σ$ tension with GR in $Σ$ (while $μ$ 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-$σ$ 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-$σ$ 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 ($μ=1$, $Σ$) is weakly favored by the data compared to $Λ$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 $Ω_{\text{DE}}(a)$, and this is clearly apparent in the high-z and high-k regime where this parameterization underestimates the deviations from GR.