Hubble drift in Palatini $f(\mathcal{R})$ theories

Abstract.

In a Palatini $f(\mathcal{R})$ model, we define chronodynamical effects due to the choice of atomic clocks as standard reference clocks and we develop a formalism able to quantitatively separate them from the usual effective dark sources one has in extended theories, namely the ones obtained by recasting field equations for $\tilde{g}$ in the form of Einstein equations. We apply the formalism to Hubble drift and briefly discuss the issue about the physical frame. In particular, we shall argue that there is not one single physical frame, for example, in the sense one defines measure in one frame while test particles goes along geodesics in the other frame. That is the physical characteristic of extended gravity. As an example, we discuss how the Jordan frame may be well suited to discuss cosmology, though it fails within the solar system.