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

Noemi Frusciante, Ryotaro Kase, Nelson J. Nunes, Shinji Tsujikawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish
Article number123517
JournalPhysical Review D
Volume98
Issue number12
DOIs
Publication statusPublished - 2018 Dec 15
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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