### Abstract

In quadratic-order degenerate higher-order scalar–tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by ϕ˙/H^{p}=constant, where ϕ˙ is the time derivative of a scalar field ϕ H is the Hubble expansion rate, and p is a constant. While the tracker is present up to the cubic-order Horndeski Lagrangian L=c_{2}X−c_{3}X^{(p−1)/(2p)}□ϕ where c_{2},c_{3} are constants and X is the kinetic energy of ϕ the DHOST interaction breaks this structure for p≠1. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state w_{ϕ}=−1−2pH˙/(3H^{2}). The scaling solution, which corresponds to p=1, is the unique case in which all the terms in the field density ρ_{ϕ} and the pressure P_{ϕ} obey the scaling relation ρ_{ϕ}∝P_{ϕ}∝H^{2}. Extending the analysis to the coupled DHOST theories with the field-dependent coupling Q(ϕ) between the scalar field and matter, we show that the scaling solution exists for Q(ϕ)=1/(μ_{1}ϕ+μ_{2}), where μ_{1} and μ_{2} are constants. For the constant Q, i.e., μ_{1}=0, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of late-time cosmic acceleration preceded by the scaling ϕ-matter-dominated epoch.

Original language | English |
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Pages (from-to) | 167-175 |

Number of pages | 9 |

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

Volume | 790 |

DOIs | |

Publication status | Published - 2019 Mar 10 |

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*,

*790*, 167-175. https://doi.org/10.1016/j.physletb.2019.01.009