## Abstract

In cubic-order Horndeski theories where a scalar field φ is coupled to nonrelativistic matter with a field-dependent coupling Q(φ), we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant Q including the case of vanishing coupling, the corresponding Lagrangian reduces to the form L=Xg2(Y)-g3(Y)□φ, where X=-∂μφ∂μφ/2 and g2, g3 are arbitrary functions of Y=Xeλφ with constant λ. We obtain the fixed points of the scaling Lagrangian for constant Q and show that the φ-matter-dominated epoch (φMDE) is present for the cubic coupling g3(Y) containing inverse power-law functions of Y. The stability analysis around the fixed points indicates that the φMDE can be followed by a stable critical point responsible for the cosmic acceleration. We propose a concrete dark energy model allowing for such a cosmological sequence and show that the ghost and Laplacian instabilities can be avoided even in the presence of the cubic coupling.

Original language | English |
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Article number | 123517 |

Journal | Physical Review D |

Volume | 98 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2018 Dec 15 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)