Existence of bootstrapped background-dependent (bimetric) gravitational theories

Establish whether there exist consistent nonlinear gravitational theories obtained via bootstrapping from linear massless spin-2 theories (such as Fierz–Pauli or WTDiff) that retain the flat spacetime metric as a background structure in the final theory, or demonstrate their nonexistence.

Background

The chapter analyzes the bootstrapping of linear spin-2 theories to nonlinear gravity, showing that General Relativity and Unimodular Gravity can arise depending on the initial gauge symmetries. It further discusses the possibility of constructing background-dependent theories where the flat metric persists as a genuine background in the nonlinear completion.

While the authors demonstrate WTDiff can be completed into Unimodular Gravity (retaining a background volume form), they do not find explicit examples where the full flat metric remains in the final theory. Determining the existence or nonexistence of such bootstrapped bimetric theories would clarify the role of background structures in constructive approaches to gravity.