### Abstract

We study the third order solutions of the cosmological density perturbations in Horndeski's most general scalar-tensor theory under the condition that the Vainshtein mechanism is at work. In this work, we thoroughly investigate the independence property of the functions describing the nonlinear mode couplings, which is also useful for models within general relativity. Then, we find that the solutions of the density contrast and the velocity divergence up to third order are characterized by six parameters. Furthermore, the one-loop order power spectra obtained with third order solutions are described by four parameters. We exemplify the behavior of the one-loop order power spectra assuming the kinetic gravity braiding model, which demonstrates that the effect of modified gravity appears more significantly in the power spectrum of the velocity divergence than the density contrast.

Original language | English |
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Article number | 104033 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 92 |

Issue number | 10 |

DOIs | |

Publication status | Published - Nov 17 2015 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*92*(10), [104033]. https://doi.org/10.1103/PhysRevD.92.104033