## 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 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.

Original language | English |
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Pages (from-to) | 2122-2131 |

Number of pages | 10 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 475 |

Issue number | 2 |

Early online date | 9 Jan 2018 |

DOIs | |

Publication status | Published - 1 Apr 2018 |

## Keywords

- Cosmological parameters
- Cosmology: observations
- Cosmology: theory
- Dark energy
- Gravitation
- Large-scale structure of Universe