Recent developments in bimetric theory
Angnis Schmidt-May, Mikael von Strauss
TL;DR
The review surveys ghost-free nonlinear spin-2 theories, centering on Hassan–Rosen bimetric theory and its dRGT predecessor, detailing how a ghost-free nonlinear potential is constructed to propagate 5 degrees of freedom for a massive graviton together with 2 for a massless graviton. It derives consistency proofs, studies Einstein vacua, mass spectra, and matter couplings, and discusses GR and massive gravity limits, including implications for cosmology and high-energy behaviour. It also examines classical solutions (black holes, cosmology), the possibility of nonlinear partial masslessness, and connections to conformal gravity, arguing both for and against PM realisations within these frameworks. Finally, the review discusses higher-dimensional extensions, Lovelock terms, multimetric and vierbein formulations, and outlines open theoretical and phenomenological challenges, with attention to quantum stability and observational prospects.
Abstract
This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of motion in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity limits of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and finally we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.