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Nunes, Noemi Frusciante, Ryotaro Kase, Shinji Tsujikawa","submitted_at":"2018-10-18T09:19:09Z","abstract_excerpt":"In cubic-order Horndeski theories where a scalar field $\\phi$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(\\phi)$, 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 $L=Xg_2(Y)-g_3(Y)\\square \\phi$, where $X=-\\partial_{\\mu}\\phi\\partial^{\\mu}\\phi/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{\\lambda \\phi}$ with constant $\\lambda$. 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