The formalism of invariants in scalar-tensor and multiscalar-tensor theories of gravitation

TL;DR

This paper reviews the formalism of invariants in scalar-tensor and multiscalar-tensor gravity theories, emphasizing how physical observables can be expressed independently of the choice of conformal frame or parametrization.

Contribution

It provides a systematic method to construct invariants in scalar-tensor theories, enabling frame-independent analysis of physical quantities.

Findings

Invariants can be constructed to describe physical observables.

Parametrized post-Newtonian parameters are expressed in terms of invariants.

Cosmological characteristics are represented using invariant functions.

Abstract

We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be presented in different conformal frames and parametrizations. Due to this freedom in transformations, the scalar fields themselves do not carry independent physical meaning (in a generic parametrization). However, there are functions of the scalar fields and their derivatives which remain invariant under the transformations, providing a set of physical variables for the theory. We indicate how to construct such invariants and show how the observables like parametrized post-Newtonian parameters and characteristics of Friedmann-Lemaitre-Robertson-Walker cosmology can be neatly expressed in terms of the invariants.