Integrability from Point Symmetries in a family of Cosmological Horndeski Lagrangians

Abstract

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lema\^ıtre-Robertson-Walker spacetime. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. \ The De Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

13 pages; new material and discussion improved; version accepted for publication by EPJC

References in corpus (11)

• Covariant Galileon
• Cosmological Solutions of $f(T)$ Gravity
• Equivalence of the Einstein and Jordan frames
• Dynamical analysis of generalized Galileon cosmology
• Noether symmetry in $f(R)$ cosmology
• Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity
• $f(R)$-gravity from Killing Tensors
• Noether analysis of Scalar-Tensor Cosmology
• Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis
• Nonlinear Ordinary Differential Equations: A discussion on Symmetries and Singularities
• On the action of the complete Brans-Dicke theory

Cited by in corpus (14)

• Noether Symmetries as a geometric criterion to select theories of gravity
• Constraints on quintessence scalar field models using cosmological observations
• Classification of the Horndeski cosmologies via Noether Symmetries
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Reduced Lagrangians and analytic solutions in Einstein-æther Cosmology
• Conservation laws and Exact Solutions in Brans-Dicke Cosmology with a Scalar Field
• Noether Symmetries in $f(T,T_G)$ Cosmology
• New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field
• Integrability of geodesic motions in curved manifolds through non-local conserved charges
• Quantum cosmology of Bianchi VIII, IX LRS geometries
• General analysis of Noether symmetries in Horndeski gravity
• Revisiting dynamics of interacting quintessence
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field