Abstract
Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom. It is widely believed that massive gravity models with six degrees of freedom have an unavoidable ghost-like instability; however, the corresponding medium has stable phonon-like excitations. The apparent contradiction is solved by the presence of a non-vanishing background pressure and energy density of the medium that opens up a stability window. The result is confirmed by looking at linear stability on an expanding Universe, recovering the flat space stability conditions in the small wavelength limit. Moreover, one can show that under rather mild conditions, no ghost-like instability is present for any wavelength. As a result, exploiting the medium interpretation, a generic massive gravity model with six degrees of freedom is perfectly viable.
Highlights
In recent years there has been a renewed interest in massive gravity, see, for instance, the reviews [1,2,3]
It turns out that when dynamical gravity is added to the game, in the unitary gauge, self-gravitating media are equivalent to massive gravity and six d.o.f. are present
Massive gravity theories with six d.o.f. on Minkowski space are plagued by ghost instabilities [4,5,1,2,3] and a great effort has been devoted trying to find a nonperturbative way to project out the unwanted sixth mode
Summary
In recent years there has been a renewed interest in massive gravity, see, for instance, the reviews [1,2,3]. One of the main issues of massive gravity is that a randomly picked model on Minkowski space propagates six degrees of freedom (d.o.f.) and among the two scalar modes one leads to ghost instabilities [4,5,1,2,3] This is the case irrespectively if the proposed theories are Lorentz invariant [4] or Lorentz breaking [6,5]. (iv) Analyzing perturbations around a FLRW background in the short wavelength limit, the same stability conditions for a medium on Minkowski spacetime are recovered This shows that massive gravity models with six d.o.f. can be intrinsically stable.
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