Ghosts in Massive Gravity

Harvard University, Cambridge, Massachusetts, United States
Journal of High Energy Physics (Impact Factor: 6.11). 05/2005; 0509(09). DOI: 10.1088/1126-6708/2005/09/003
Source: arXiv


In the context of Lorentz-invariant massive gravity we show
that classical solutions around heavy sources are plagued by ghost
instabilities. The ghost shows up in the effective field theory at
huge distances from the source, much bigger than the Vainshtein
radius. Its presence is independent of the choice of the non-linear
terms added to the Fierz-Pauli lagrangian. At the Vainshtein radius
the mass of the ghost is of order of the inverse radius, so that the
theory cannot be trusted inside this region, not even at the
classical level.

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    • "In particular, we will be interested in the high energy limit in which the mass of the spin-2 mode goes to zero while keeping various non-linear scales fixed. In the case of a pure massive spin-2, this limit is greatly simplified using the Stückelberg formulation, in which new fields and gauge symmetries are introduced in order to more easily see the non-linear dynamics of the longitudinal modes of the massive spin- 2 [19] [20] [21] [22] [23] (see [24] [25] for reviews). In particular, this formalism has been instrumental in finding fully non-linear theories [26] free [27] from Boulware-Deser modes [28]. "
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    ABSTRACT: Curvature squared terms, when added to the Einstein-Hilbert action and treated non-perturbatively, generically result in the propagation of an extra massive scalar state and an extra massive spin-2 ghost state. Using the Stueckelberg trick, we study the high-energy limit in which the mass of the spin-2 state is taken to zero, with strong-coupling scales held fixed. The Stueckelberg approach makes transparent the interplay between the ghost graviton and the healthy graviton which allows the theory to evade the usual Lambda 3 strong coupling scale of massive gravity and become renormalizable, at the expense of stability.
    Preview · Article · Aug 2015
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    • "In fact, in first order form a qualitatively new problem can arise. In massive gravity, the standard problem is the Boulware–Deser (BD) ghost [38], see also [39] [40]. "
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    ABSTRACT: We reconsider the possibility of a class of new kinetic terms in the first order (vielbein) formulation of massive gravity and multi-gravity. We find that new degrees of freedom emerge which are not associated with the Boulware--Deser ghost and are intrinsic to the vielbein formulation. These new degrees of freedom are associated with the Lorentz transformations which encode the additional variables contained in the vielbein over the metric. Although they are not guaranteed to be ghostly, they are nevertheless infinitely strongly coupled on Minkowski spacetime and are not part of the spin-2 multiplet. Hence their existence implies the uniqueness of the Einstein--Hilbert term as the kinetic term for a massive graviton.
    Preview · Article · May 2015 · Classical and Quantum Gravity
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    • "Under the scalar field redefinition [36] [37] χ = c m 2 φ, "
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    ABSTRACT: We study higher derivative terms associated to an scalar field cosmology. We consider a coupling between the scalar field and the geometry inspired in the Pais-Uhlenbeck oscillator given by $\alpha\partial_{\mu}\partial^{\mu}\phi\partial_{\nu}\partial^{\nu}\phi.$ We investigate the cosmological dynamics in a phase space. For $\alpha>0$ we provide conditions for the stability of de Sitter solutions. For $\alpha<0,$ which is the portion of the parameter space where the crossing of the phantom divide $w_{DE}=-1$ and the cyclic behavior are possible, we present regions in the parameter space where the ghost has benign or malicious behavior, according to Smilga's classification.
    Full-text · Article · Aug 2014 · Journal of Cosmology and Astroparticle Physics
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