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 parametrise the growth of structure using the growth index $\gamma$, finding $\gamma=0.566\pm0.058$ (68\% C.L.). Second, 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 dependency of $G_M$ and $G_L$ as well as binning in redshift space, introducing four additional degrees of freedom, $G_M(z<0.5)$, $G_M(z>0.5)$, $G_L(z<0.5)$, $G_L(z>0.5)$. At 68\% C.L. we measure $G_M=0.980 \pm 0.096$ and $G_L=1.082 \pm 0.060$ for a linear model, $G_M= 1.01\pm 0.36$ and $G_L=1.31 \pm 0.19$ for a cubic model as well as $G_M(z<0.5)=1.26 \pm 0.32$, $G_M(z>0.5)=0.986\pm0.022$, $G_L(z<0.5)=1.067\pm0.058$ and $G_L(z>0.5)=1.037\pm0.029$. 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 $B_0< 7.7 \times 10^{-5}$ (95\% C.L). For all models we considered we find good agreement with general relativity.