Covariant conserved currents for scalar-tensor Horndeski theory

TL;DR

This paper extends the formalism of covariant conserved currents to the general Horndeski scalar-tensor theory, providing a systematic way to derive conserved quantities in these models, including perturbations.

Contribution

It introduces covariant conserved currents for all four Lagrangians of Horndeski theory, extending previous methods from general relativity to this broader class of scalar-tensor theories.

Findings

Derived covariant conserved currents for all four Horndeski Lagrangians.

Constructed a superpotential leading to conserved currents in Brans-Dicke theory.

Extended conservation law formalisms to scalar-tensor perturbations.

Abstract

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar field. As a specific illustration we derive a superpotential which leads to the covariantly conserved current in the Branse-Dicke theory.