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We use measurements from the Planck satellite mission and galaxy redshiftsurveys over the last decade to test three of the basic assumptions of thestandard model of cosmology, $\Lambda$CDM: the spatial curvature of theuniverse, the nature of dark energy and the laws of gravity on large scales. Weobtain improved constraints on several scenarios that violate one or more ofthese 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-dependentequation of state, which is an improvement over current best constraints\citep{Aubourg2014}. In the context of modified gravity, we consider popularscalar tensor models as well as a parametrization of the growth factor. In thecase of one-parameter $f(R)$ gravity models with a $\Lambda$CDM background, weconstrain $B_0 < 1.36 \times 10^{-5} $ (1$\sigma$ C.L.), which is animprovement by a factor of 4 on the current best \citep{XU2015}. We provide thevery first constraint on the coupling parameters of general scalar-tensortheory and stringent constraint on the only free coupling parameter ofChameleon 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 $\gamma = 0.612 \pm 0.072$ (11.7\%measurement) for growth index parametrization. We improve all the currentconstraints by combining results from various galaxy redshift surveys in acoherent way, which includes a careful treatment of scale-dependence introducedby modified gravity.

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