be independent of the conformal representation, its interpretation is not.

There are results in cosmology in which the universe accelerates in one frame but not in the other. From the pragmatic point of view of an astronomer attempting to fit observational data (for example, type Ia supernovae data to a model of the present acceleration of the universe), the two frames certainly do not appear to be “physically equivalent” [@nodicap2; @CapozzielloPrado].

To approach correctly the problem of physical equivalence under conformal transformations, one has to compare physics in different conformal frames at the level of the Lagrangian, of the field equations, and of their solutions [@allemandi]. This comparison may not always be easy but, in certain cases, it is extremely useful to discriminate between frames. It has been adopted, for example, in Ref. [@cno], to compare cosmological models in the Einstein and the Jordan frame. Specifically, it has been shown that solutions of $f(R)$ and scalar-tensor gravity cannot be assumed to be physically equivalent to those in the Einstein frame when matter fields are given by generalized Equations of State.

In these and in other situations, one must specify precisely what “physical equivalence” means. In certain situations physical equivalence is 