### Abstract

In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling Geff associated with the growth rate of matter perturbations as well as the effective gravitational potential Geff relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.

Original language | English |
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Pages (from-to) | 123-133 |

Number of pages | 11 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 706 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2011 Dec 6 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*706*(2-3), 123-133. https://doi.org/10.1016/j.physletb.2011.11.028