Slice Energy and Conformal Frames in Theories of Gravitation

Abstract

We examine and compare the behaviour of the scalar field slice energy in different classes of theories of gravity, in particular higher-order and scalar-tensor theories. We find a universal formula for the energy and compare the resulting conservation laws with those known in general relativity. This leads to a comparison between the inflaton, the dilaton and other forms of scalar fields present in these generalized theories. It also shows that all such conformally-related, generalized theories of gravitation allow for the energy on a slice to be invariably defined and its fundamental properties be insensitive to conformal transformations.