Abstract. We consider the cosmological models based on Palatini f (R)-theory for the function f (R) = αR − 2 β R2 − 3R γ , which, when only dust visible matter is considered, is called dune cosmology in view of the shape of the function f (R(a)) (being a the scale factor). We discuss the meaning of solving the model, and interpret it according to the Ehlers-Pirani-Schild framework as defining a Weyl geometry on spacetime.
Accordingly, we extend the definitions of luminosity distance, proper distance, and red-shift to Weyl geometries and fit the values of parameters to SNIa data. Since the theoretical prediction is model-dependent, we argue that the fit is affected by an extra choice, namely a model for atomic clocks, which, in principle, produces observable effects. To the best of our knowledge, these effects have not being considered in the literature before.