(Non?)-Equivalence of Einstein and Jordan frames in quantized cosmological models.- [PDF] - [Article]

Sachin Pandey, Sridip Pal, Narayan Banerjee

The present work sheds light on the nature of mathematical equivalence of Jordan frame and its conformally transformed version, the Einstein frame, as far as Brans-Dicke theory is concerned. It is shown that question of equivalence surviving a quantization of cosmological models in the theory is intricately related to whether the canonical structure breaks down while going from one frame to the other. It is found that that the consistent operator ordering to make two frames equivalent requires a non-canonical transformation that mixes gravity sector with scalar sector to undo the non minimal coupling, present in Jordan frame. The question of equivalence thus depends on the details of quantization prescriptions, i.e. whether we are allowed to make any such non-canonical transformation at classical level before quantizing the theory. We work with the Wheeler-deWitt quantization scheme and take up quite a few anisotropic cosmological models as examples.