Effective Energy-Momentum Tensors and Conformal Frames

Abstract

The conformal transformations presented in the previous chapter establish a mathematical equivalence between scalar-tensor theories and Einstein’s general relativity, with the modifications dictated by the anomalous coupling of the Einstein frame scalar to ordinary matter and its consequences. A priori, the mathematical equivalence need not be a physical one. The literature using conformal transformations in cosmology and in alternative theories of gravity is plagued by confusion and ambiguity on the issue of the physical equivalence of the two conformal frames, or which frame should be regarded as the physical one. As a consequence, the conformal transformation technique is often misused and its results are given erroneous interpretations. Incompatible points of view occurring in the literature support the following ideas [613, 363] :

• (first viewpoint) that the Jordan and the Einstein frame are physically equivalent,

• (second viewpoint) that the two frames are inequivalent the Jordan frame is the physical one, and the Einstein frame is unphysical,

• (third viewpoint) that the two frames are inequivalent — the Jordan frame is unphysical, and the Einstein frame is physical.