### Abstract

We derive the equation of matter density perturbations on subhorizon scales for a general Lagrangian density f(R, ,X) that is a function of a Ricci scalar R, a scalar field , and a kinetic term X=-( )2/2. This is useful to constrain modified gravity dark energy models from observations of large-scale structure and weak lensing. We obtain the solutions for the matter perturbation δm as well as the gravitational potential Φ for some analytically solvable models. In an f(R) dark energy model with the Lagrangian density f(R)=αR1+m-Λ, the growth rates of perturbations exhibit notable differences from those in the standard Einstein gravity unless m is very close to 0. In scalar-tensor models with the Lagrangian density f=F( )R+2p( ,X), we relate the models with coupled dark energy scenarios in the Einstein frame and reproduce the equations of perturbations known in the current literature by making a conformal transformation. We also estimate the evolution of perturbations in both Jordan and Einstein frames when the energy fraction of dark energy is constant during the matter-dominated epoch.

Original language | English |
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Article number | 023514 |

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

Volume | 76 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Jul 25 |

Externally published | Yes |

### ASJC Scopus subject areas

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