Invariant quantities in the multiscalar-tensor theories of gravitation

TL;DR

This paper develops invariant quantities in multiscalar-tensor gravity theories, providing a framework to compare Einstein and Jordan frames and ensuring consistent post-Newtonian results across frames.

Contribution

It introduces invariant objects and translation rules that unify descriptions in different frames of multiscalar-tensor gravity theories.

Findings

Invariant quantities are constructed under Weyl rescaling.

Translation rules relate Einstein and Jordan frames.

Post-Newtonian results are consistent across frames.

Abstract

The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the scalar fields are redefined. We introduce rules to construct further such objects and put forward a scheme that allows to express the results obtained either in the Einstein frame or in the Jordan frame as general ones. These so called translation rules are used to show that the parametrized post-Newtonian approximation results obtained in the aforementioned two frames indeed are the same if expressed in a general frame.