Ghost-free massive gravity with a general reference metric

By Sayed Fawad Hassan, Rachel A Rosen, A. Schmidt-May. 2011

427 citations recorded by the source corpus.

A bstractTheories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c8a3eb527a60ab5c6f96ea0b82f4a0870cc2fbcc

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Citations in the corpus

Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality (2012, methodology): “A generalization to having two free and dynamic metrics in the formulation was then proposed and showed a theoretically viable option by Hassan and Rosen in [29, 30, 31].”
Universal Resistivity from Holographic Massive Gravity (2013, background): “Recently, a class of non-linear massive gravity theories has been proposed [20, 21] in which the ghost field is absent [22, 23].”
Heavy spin-2 Dark Matter (2016, background): “Only recently has the unique description which avoids the ghost been found [10–13].”
Momentum relaxation in holographic massive gravity (2013, background): “he symmetries associated with reparameterisations ofthe spatial x,y co-ordinates and will result in the dissipation ofmomentum (butnot energy) in the dual ﬁeld theory. It was shown in [21], following [29], that the Boulware-Deser ghost [22] may be absent in this theory (see [30] for a pedagogical re”
Interacting spin-2 fields (2012, background): “fμν , and the theory is still ghost-free [17].”
Thermodynamics of Black Holes in Massive Gravity (2014, background): “In [14, 15, 16], a classical of nonlinear massive gravity theories has been proposed, in which the ghost field is absent [17, 18].”
Massive Gravity (2014, background): “This corresponds to a theory of massive gravity on a more general reference metric as presented in [296].”
Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity (2014, methodology): “Models such as Dvali-Gabadadze-Porrati (DGP) gravity [53] or ghost-free massive gravity [54–56] lie outside of our purview.”