Non-Fierz-Pauli bimetric theory from quadratic curvature gravity on Einstein manifolds

TL;DR

This paper demonstrates that in four-dimensional Einstein manifolds, quadratic-curvature gravity can be decomposed into massless and massive components, revealing a non-Fierz-Pauli structure and connecting observational bounds to theoretical parameters.

Contribution

It introduces a novel decomposition of quadratic-curvature gravity into massless and massive sectors, including a non-Fierz-Pauli massive gravity component, on Einstein manifolds.

Findings

Massless and massive degrees of freedom can be decoupled in quadratic-curvature gravity.

The massive sector resembles non-Fierz-Pauli-type massive gravity.

Observational bounds constrain the coupling constants in the theory.

Abstract

We show that, in four-dimensional spacetimes with an arbitrary Einstein metric, with and without a cosmological constant, perturbative dynamical degrees of freedom in generic quadratic-curvature gravity can be decoupled into massless and massive parts. The massive part has the structure identical to, modulo the over-all sign, the non-Fierz-Pauli-type massive gravity, and a further decomposition into the spin-2 and spin-0 sectors can be done. The equivalence at the level of equations of motion allows us to translate various observational bounds on the mass of extra fields into constraints on the coupling constants in quadratic curvature gravity. We find that the Weyl-squared term is confronting two apparently contradicting constraints on massive spin-2 fields from the inverse-square law experiments and observations of spinning black holes.