Classification of the Horndeski cosmologies via Noether Symmetries

TL;DR

This paper uses Noether symmetries to classify and solve Horndeski cosmological models, enabling the derivation of exact solutions and connecting to various modified gravity theories.

Contribution

It introduces a symmetry-based classification method for Horndeski cosmologies and derives exact solutions, linking them to other modified gravity theories.

Findings

Classification of Horndeski models via Noether symmetries

Derivation of exact cosmological solutions

Connection to $f(R)$, Brans-Dicke, and string-inspired gravity

Abstract

Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like $f(R)$ gravity, Brans-Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out.