Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy
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 =X g2(Y )-g3(Y )□ϕ , where X =-∂μϕ ∂μϕ /2 and g2 , g3 are arbitrary functions of Y =X eλ ϕ 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 g3(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.
- 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
- E-Print:
- 17 pages, 3 figures, version to appear in Physical Review D