Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames

Abstract

Owing to it's non-minimal nature of coupling with gravity, the scalar field in a scalar-tensor theory is covariantly conserved with more than one choice of its energy-momentum tensor (EMT). Apparently this ambiguity in the choice of the symmetric EMT results from the way the conserved EMT is identified by different algebraic manipulations of the gravity field equation in such nonminimally coupled (NMC) theories. In this paper, we demonstrate that one can arrive at these different choices of EMT, not by mere algebraic manipulation, but by demanding the equivalence of a NMC theory in Jordan frame with a minimally coupled theory in Einstein frame at the level of physical laws.