  The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside
the vacuum solutions of the non-linear formulations of massive gravity in the
same spirit of the $\sigma$-models. When the gravitational effects are taken
into account, and the observers are located at any distance with respect to the
source, this degeneracy corresponds to a multiplicity (flow) of the fundamental
scales of the theory. The different values of the fundamental scales are
connected each other through the broken generators of the theory.
