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

Abstract

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 modi ed gravity: First, we parametrise the growth of structure using the growth index, nding = 0:566 0:058 (68% C.L.). Second, we modify the relation of the two Newtonian potentials by introducing two additional parameters, GM and GL. In this approach, GM refers to modi cations of the growth of structure whereas GL to modi cation of the lensing potential. We consider a power law to model the redshift dependency of GM and GL as well as binning in redshift space, introducing four additional degrees of freedom, GM(z < 0:5), GM(z > 0:5), GL(z < 0:5), GL(z > 0:5). At 68% C.L. we measure GM = 0:980 0:096 and GL = 1:082 0:060 for a linear model, GM = 1:01 0:36 and GL = 1:31 0:19 for a cubic model as well as GM(z < 0:5) = 1:26 0:32, GM(z > 0:5) = 0:986 0:022, GL(z < 0:5) = 1:067 0:058 and GL(z > 0:5) = 1:037 0:029. Thirdly, we investigate general scalar tensor theories of gravity, nding 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% C.L). For all models we considered we nd good agreement with general relativity.