  In this work we examine what are the cosmological implications of allowing
the geometrical curvature density to behave independently from the energy
density contents. Using the full data extracted by Planck mission from CMB,
combined with BAO and SNIa measurements, we derive, in the light of this
approach, new constraints on the cosmological parameters. In particular we
determine the behavior of the curvature dark energy degeneracy when allowing a
varying equation of state for the latter. We also examine whether this approach
could bridge the gap recently found between the Hubble parameter value
determined from CMB and that from the local universe measurements
