Jordan and Einstein frames

The Lagrangian in scalar-tensor theory can be expressed in the Jordan frame in which the scalar field or some function of it multiplies the Ricci scalar, or in the Einstein frame in which Ricci scalar is not multiplied by the scalar field. There exist various transformations between these frames. Despite the fact that these frames have been around for some time there has been debate about whether either, both, or neither frame is a 'physical' frame which can be compared to observations and experiment.

Christopher Hill and Graham Ross have shown that there exist ``gravitational contact terms" in the Jordan frame, whereby the action is modified by graviton exchange. This modification leads back to the Einstein frame as the effective theory. Contact interactions arise in Feynman diagrams when a vertex contains a power of the exchanged momentum, ${\displaystyle q^{2}}$, which then cancels against the Feynman propagator, ${\displaystyle 1/q^{2}}$, leading to a point-like interaction. This must be included as part of the effective action of the theory. When the contact term is included results for amplitudes in the Jordan frame will be equivalent to those in the Einstein frame, and results of physical calculations in the Jordan frame that omit the contact terms will generally be incorrect. This implies that the Jordan frame action is misleading, and the Einstein frame is uniquely correct for fully representing the physics.