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arXiv · 1810.07957

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
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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 $L=Xg_2(Y)-g_3(Y)\square ϕ$, where $X=-\partial_μϕ\partial^μϕ/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{λϕ}$ with constant $λ$. We obtain the fixed points of the scaling Lagrangian for constant $Q$ and show that the $ϕ$-matter-dominated-epoch ($ϕ$MDE) is present for the cubic coupling $g_3(Y)$ containing inverse power-law functions of $Y$. The stability analysis around the fixed points indicates that the $ϕ$MDE 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.

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Noemi Frusciante, Ryotaro Kase, Nelson J. Nunes, Shinji Tsujikawa. 2018-12-15. Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy. https://doi.org/10.1103/physrevd.98.123517

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