Structures in multiple spin-2 interactions

Abstract

We study generalisations of ghost-free bimetric theory which involve more than two spin-2 fields. The consistent interactions can enter in the form of two different couplings and in the majority of this work we concentrate on the simpler one. The corresponding action involves one metric coupled to $N$ tensor fields which do not interact with each other. We derive maximally symmetric solutions to the multimetric equations of motion and identify the mass eigenstates in the linearised theory around these backgrounds. Our results are then applied to the problem of singling out multimetric models which possess certain additional structures. In particular, we look for a relation between scale invariant background solutions, the perturbative emergence of Weyl invariance and the presence of partially massless spin-2 fields in the linear theory. Our findings generalise known results in bimetric theory and allow us to point out similarities and differences between the bi- and multimetric models.

40 pages, 4 figures; typos in eq. (3.24) and (3.37) fixed

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• Resummation of Massive Gravity
• Interacting Spin-2 Fields
• No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
• Massive gravity from bimetric gravity
• Particular Solutions in Bimetric Theory and Their Implications
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• Partially Massless Higher-Spin Theory
• A non-linear extension of the spin-2 partially massless symmetry
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Cited by in corpus (9)

• Higher dimensional massive bigravity
• Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity
• Interactions of multiple spin-2 fields beyond pairwise couplings
• Black Holes in Multi-Metric Gravity
• Aller guten Dinge sind drei: Cosmology with three interacting spin-2 fields
• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Black Holes in Multi-Metric Gravity II: Hairy Solutions and Linear Stability of the Non- and Partially Proportional Branches
• Gravitational wave propagation in bigravity in the late universe
• Categorical generalization of BF theory coupled to gravity