@article{0508ef22eb714f5083ae4172331debf2,

title = "Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy",

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.",

author = "Noemi Frusciante and Ryotaro Kase and Nunes, {Nelson J.} and Shinji Tsujikawa",

note = "Funding Information: We thank Luca Amendola, Guillem Dom{\`e}nech, and Adalto R. Gomes for useful correspondence. The research of N. F. and N. J. N. is supported by Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (FCT) through national funds (Grant No. UID/FIS/04434/2013), by FEDER through COMPETE2020 (Grant No. POCI-01-0145-FEDER-007672) and by FCT project “DarkRipple—Spacetime ripples in the dark gravitational Universe” with Grant No. PTDC/FIS- OUT/29048/2017. N. J. N. is also supported by an FCT Research contract, with Grant No. IF/00852/2015. R. K. is supported by the Grant-in-Aid for Young Scientists B of the JSPS Grant No. 17K14297. S. T. is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS Grant No. 16K05359 and MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Cosmic acceleration” (Grant No. 15H05890). Publisher Copyright: {\textcopyright} 2018 American Physical Society.",

year = "2018",

month = dec,

day = "15",

doi = "10.1103/PhysRevD.98.123517",

language = "English",

volume = "98",

journal = "Physical Review D",

issn = "2470-0010",

publisher = "American Physical Society",

number = "12",

}