# Tracker and scaling solutions in DHOST theories

Research output: Contribution to journal › Article

In quartic-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*=constant, where^{p}*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*wφ*=−1−2*pH˙*/(3*H*^{2}). The scaling solution, which corresponds to*p*=1, is the unique case in which all the terms in the field density*ρφ*and the pressure*Pφ*obey the scaling relation*ρφ*∝*Pφ*∝*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 | Physical Letters B |

Volume | 790 |

Early online date | 17 Jan 2019 |

DOIs | |

Publication status | Published - 10 Mar 2019 |

### Documents

- 1-s2.0-S0370269319300255-main
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Licence: CC BY

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