General analysis of Noether symmetries in Horndeski gravity

TL;DR

This paper systematically analyzes Noether symmetries within Horndeski gravity, revealing how these symmetries are preserved or altered across various scalar-tensor theories and in the presence of matter.

Contribution

It extends the classification of Noether symmetries to the full Horndeski gravity framework, including non-minimal couplings and matter effects.

Findings

Noether symmetries are preserved in the presence of matter.

The classification applies to kinetic gravity braiding and extended cuscuton models.

Selected Horndeski functions remain unchanged with matter presence.

Abstract

We explore Noether symmetries of Horndeski gravity, extending the classification of general scalar-tensor theories. Starting from the minimally coupled scalar field and the first-generation scalar-tensor gravity, the discussion is generalised to kinetic gravity braiding and Horndeski gravity. We highlight the main findings by focusing on the non-minimally coupled Gauss-Bonnet term and the extended cuscuton model. Finally, we discuss how the presence of matter can influence Noether symmetries. It turns out that the selected Horndeski functions are unchanged with respect to the vacuum case.