Recent developments in bimetric theory

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.

Hybrid theory of gravity

“…In the same manner, we also find that |g 00 | − g −1 11 vanishes in the small mass limit µ → 0, up to this order. These asymptotic behaviors show a different case from the bigravity theory with two tensor fields [3,31].…”

“…This form is known as the safest and most interesting choice in bigravity theories for cosmology [3,32]. It is often referred to as a "twin matter" model.…”

“…Bigravity theory is an alternative theory of gravity that describes both massless and massive gravitons [1,2] (for a review, see [3]). The low-energy modification from General Relativity (GR) is expected to explain mysterious components of the universe known as dark matter and dark energy.…”

“…3 In this theory, the dynamics of gravity is described by a single scalar field. A normalized derivative of the scalar field expresses part of the dynamical metric, as well as the scalar field itself.…”

“…2 For the various models of modified gravity and their cosmological meanings, see [15][16][17]. 3 See also [24,25]. theory naturally possesses a massless mode for the symmetric tensor field and yields the Schwarzschild solution exactly.…”