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 $\varphi$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(\varphi )$, 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 $L=X{g}_2(Y)-g_3(Y)\square \varphi$, where $X=-{\partial }_{\mu }\varphi {\partial }^{\mu }\varphi /2$ and $g_2,g_3$ are arbitrary functions of $Y=X{e}^{\lambda \varphi }$ with constant $\lambda$. We obtain the fixed points of the scaling Lagrangian for constant $Q$ and show that the $\varphi$-matter-dominated-epoch ($\varphi$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 $\varphi$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.

17 pages, 3 figures, version to appear in Physical Review D

References in corpus (11)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Cosmology and the Fate of Dilatation Symmetry
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data
• Challenges for scaling cosmologies
• Cosmological Scaling Solutions and Cross-coupling Exponential Potential
• Assisted coupled quintessence

Cited by in corpus (13)

• Scalar-field dark energy nonminimally and kinetically coupled to dark matter
• Scaling solutions and weak gravity in dark energy with energy and momentum couplings
• Tracker and scaling solutions in DHOST theories
• Conformally Coupled Tachyonic Dark Energy
• Coupled vector dark energy
• Improving data-driven model-independent reconstructions and updated constraints on dark energy models from Horndeski cosmology
• Growth of non-linear structures and spherical collapse in the Galileon Ghost Condensate model
• Coupled quintessence with a generalized interaction term
• Dissecting kinetically coupled quintessence: phenomenology and observational tests
• Self-tuning kinetic gravity braiding: Cosmological dynamics, shift symmetry, and the tadpole
• Stealth black hole perturbations in kinetic gravity braiding
• Constraining cosmological scaling solutions of a Galileon field
• Gravitational wave signatures from dark sector interactions