Most general cubicorder Horndeski Lagrangian allowing for scaling solutions and the application to dark energy
Abstract
In cubicorder Horndeski theories where a scalar field ϕ is coupled to nonrelativistic matter with a fielddependent 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 =X g_{2}(Y )g_{3}(Y )□ϕ , where X =∂_{μ}ϕ ∂^{μ}ϕ /2 and g_{2} , g_{3} are arbitrary functions of Y =X e^{λ ϕ} with constant λ . We obtain the fixed points of the scaling Lagrangian for constant Q and show that the ϕ matterdominated epoch (ϕ MDE ) is present for the cubic coupling g_{3}(Y ) containing inverse powerlaw 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.
 Publication:

Physical Review D
 Pub Date:
 December 2018
 DOI:
 10.1103/PhysRevD.98.123517
 arXiv:
 arXiv:1810.07957
 Bibcode:
 2018PhRvD..98l3517F
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 17 pages, 3 figures, version to appear in Physical Review D