  Scale invariant (transverse) gravitational theories are introduced. They are
invariant under pure metric rescalings (i.e. the matter fields are inert under
those). This symmetry forbids the presence of a cosmological constant. Those
theories are not invariant under the full set of diffeomorphisms, but only with
respect to those locally characterized by the fact that their generator is
transverse $\pd_\a \xi^\a=0$.
