Recent developments in bimetric theory

TL;DR

This review summarizes recent progress in ghost-free bimetric theory, covering its history, mathematical consistency, solutions, cosmology applications, and potential extensions, highlighting its significance in massive gravity research.

Contribution

It provides a comprehensive overview of recent developments in ghost-free bimetric theory, including new solutions, stability proofs, and connections to other gravity theories.

Findings

Analysis of Einstein solutions and mass spectrum in bimetric theory

Discussion of matter couplings and gravity limits

Overview of cosmological solutions and extensions

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.