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

N. Frusciante, R. Kase, N. J. Nunes, S. Tsujikawa

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.

Keywords
General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics; High Energy Physics - Phenomenology

Physical Review D
Volume 98, Issue 12
2018 December

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia