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Testing deviations from $Λ$CDM with growth rate measurements from 6 Large Scale Structure Surveys at $\mathbf{z=0.06}$ to 1

We use measurements from the Planck satellite mission and galaxy redshift surveys over the last decade to test three of the basic assumptions of the standard model of cosmology, $Λ$CDM: the spatial curvature of the universe, the nature of dark energy and the laws of gravity on large scales. We obtain improved constraints on several scenarios that violate one or more of these assumptions. We measure $w_0=-0.94\pm0.17$ (18\% measurement) and $1+w_a=1.16\pm0.36$ (31\% measurement) for models with a time-dependent equation of state, which is an improvement over current best constraints \citep{Aubourg2014}. In the context of modified gravity, we consider popular scalar tensor models as well as a parametrization of the growth factor. In the case of one-parameter $f(R)$ gravity models with a $Λ$CDM background, we constrain $B_0 < 1.36 \times 10^{-5} $ (1$σ$ C.L.), which is an improvement by a factor of 4 on the current best \citep{XU2015}. We provide the very first constraint on the coupling parameters of general scalar-tensor theory and stringent constraint on the only free coupling parameter of Chameleon models. We also derive constraints on extended Chameleon models, improving the constraint on the coupling by a factor of 6 on the current best \citep{Hojjati2011} . We also measure $γ= 0.612 \pm 0.072$ (11.7\% measurement) for growth index parametrization. We improve all the current constraints by combining results from various galaxy redshift surveys in a coherent way, which includes a careful treatment of scale-dependence introduced by modified gravity.