metric emerges later. Hence there is no obvious reason to expect only a single massless spin two field. For a large class of models built from field theory fluctuations around a linearized background [@BarLibVisb], for instance, many “gravitons” appear, and the imposition of an ad hoc symmetry [@Sindonib] is the only known way to force universality. In models of composite gravitons, a similar multiplicity of potential metrics occurs [@Wetterich4]. One can argue that if the effective action is invariant under diffeomorphisms and local Lorentz transformations, only one such field will remain massless, with the others acquiring large masses [@Wetterich4]—typically on the order of the Planck mass, although approximate symmetries can make them smaller [@Damour2]. The requirement of exact invariance is, of course, a very strong one: strong enough, in fact, to *forbid* more than one massless graviton [@Boulanger]. But this solution is also problematic, since most models with massive spin two fields are sick, containing negative energy Boulware-Deser ghosts [@BD]. While a few exceptions exist [@Hinterbichler; @deRham; @Hassan; @RRosen], these require a very special form of the action, and it is not at all clear how such a feature would emerge from a more primitive model.

Once one has a 