Question of quantum equivalence between Jordan frame and Einstein frame .

We investigate the equivalence between two different parametrizations of fields in cosmology - the so-called Jordan frame and Einstein frame - in the framework of a general scalar-tensor theory. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We therefore explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide and hence induce an off-shell dependence on the parametrization. An explanation of the origin of this frame dependence is suggested to be found within a geometrical approach in the more general field theoretical framework. Finally, we discuss the physical implications of this analysis and its consequences for cosmology.