  In this work we study the phenomenological consequences of the dependence of
mass varying neutrinos on the neutrino density in the Sun, which we precisely
compute in each point along the neutrino trajectory. We find that a generic
characteristic of these scenarios is that they establish a connection between
the effective Delta m^2 in the Sun and the absolute neutrino mass scale. This
does not lead to any new allowed region in the oscillation parameter space. On
the contrary, due to this effect, the description of solar neutrino data
worsens for large absolute mass. As a consequence a lower bound on the level of
degeneracy can be derived from the combined analysis of the solar and KamLAND
data. In particular this implies that the analysis favours normal over inverted
mass orderings. These results, in combination with a positive independent
determination of the absolute neutrino mass, can be used as a test of these
scenarios together with a precise determination of the energy dependence of the
survival probability of solar neutrinos, in particular for low energies.
