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