  The debate on the physical relevance of conformal transformations can be
faced by taking the Palatini approach into account to gravitational theories.
We show that conformal transformations are not only a mathematical tool to
disentangle gravitational and matter degrees of freedom (passing from the
Jordan frame to the Einstein frame) but they acquire a physical meaning
considering the bi-metric structure of Palatini approach which allows to
distinguish between spacetime structure and geodesic structure. Examples of
higher-order and non-minimally coupled theories are worked out and relevant
cosmological solutions in Einstein frame and Jordan frames are discussed
showing that also the interpretation of cosmological observations can
drastically change depending on the adopted frame.
