The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: constraining modified gravity

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 B₀ < 7.7 × 10^-5 (95 per cent C.L). For all models we considered, we find good agreement with general relativity.