ALBERT

Description: We use baryon acoustic oscillation and redshift space distortion from the completed Baryon Oscillation Spectroscopic Survey, corresponding to Data Release 12 of the Sloan Digital Sky Survey, combined sample analysis in combination with cosmic microwave background, supernova, and redshift space distortion measurements from additional spectroscopic surveys to test deviations from general relativity. We present constraints on several phenomenological models of modified gravity: First, we parametrize the growth of structure using the growth index γ, finding γ = 0.566 ± 0.058 (68 per cent C.L.). Secondly, we modify the relation of the two Newtonian potentials by introducing two additional parameters, G M and G L . In this approach, G M refers to modifications of the growth of structure whereas G L to modification of the lensing potential. We consider a power law to model the redshift dependence of G M and G L as well as binning in redshift space, introducing four additional degrees of freedom, G M ( z  〈 0.5), G M ( z  〉 0.5), G L ( z  〈 0.5), and G L ( z  〉 0.5). At 68 per cent C.L., we measure G M  = 0.980 ± 0.096 and G L  = 1.082 ± 0.060 for a linear model, G M  = 1.01 ± 0.36 and G L  = 1.31 ± 0.19 for a cubic model as well as G M ( z  〈 0.5) = 1.26 ± 0.32, G M ( z  〉 0.5) = 0.986 ± 0.022, G L ( z  〈 0.5) = 1.067 ± 0.058, and G L ( z  〉 0.5) = 1.037 ± 0.029. Thirdly, we investigate general scalar tensor theories of gravity, finding the model to be mostly unconstrained by current data. Assuming a one-parameter f ( R ) model, we can constrain B 0  〈 7.7 × 10 −5 (95 per cent C.L). For all models we considered, we find good agreement with general relativity.