Invariant quantities in the multiscalar-tensor theories of gravitation

Understand

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.