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.
