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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.