Equivalence of Einstein and Jordan frames in quantized anisotropic cosmological models

Abstract

The present work shows that the mathematical equivalence of the Jordan frame and its conformally transformed version, the Einstein frame, so as far as Brans–Dicke theory is concerned, survives a quantization of cosmological models, arising as solutions to the Brans–Dicke theory. We work with the Wheeler–deWitt quantization scheme and take up quite a few anisotropic cosmological models as examples. We effectively show that the transformation from the Jordan to the Einstein frame is a canonical one and hence two frames furnish equivalent description of same physical scenario.