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 is currently heated debate about whether either, both, or neither frame is a 'physical' frame which can be compared to observations and experiment.
Contents
Equations and physical interpretation
If we perform the Weyl rescaling
As an example consider the transformation of a simple Scalar-tensor action with an arbitrary set of matter fields
The tilde fields then correspond to quantities in the Jordan frame and the fields without the tilde correspond to fields in the Einstein frame. See that the matter action
The Jordan and Einstein frames are constructed to render certain parts of physical equations simpler which also gives the frames and the fields appearing in them particular physical interpretations. For instance, in the Einstein frame, the equations for the gravitational field will be of the form
I.e., they can be interpreted as the usual Einstein equations with particular sources on the right-hand side. Similarly, in the Newtonian limit one would recover the Poisson equation for the Newtonian potential with separate source terms.
However, by transforming in the Einstein frame the matter fields are now not coupled simply to the background but also to the field
where
On the other hand, in the Jordan frame, all the matter fields
Models
Jordan frame gravity can be used to calculate type IV singular bouncing cosmological evolution, to derive the type IV singularity.