Abstract
We study the first cosmological implications of the mimetic theory of massive gravity recently proposed by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which additionally contains a mimetic dark matter component. In an echo of other modified gravity theories, there are self-accelerating solutions which contain a ghost instability. In the ghost-free region of parameter space, the effect of the graviton mass on the cosmic expansion history amounts to an effective negative cosmological constant, a radiation component, and a negative curvature term. This allows us to place constraints on the model parameters—the graviton mass and the Stückelberg vacuum expectation value—by insisting that the effective radiation and curvature terms be within observational bounds. The late-time acceleration must be accounted for by a separate positive cosmological constant or other dark energy sector. We impose further constraints at the level of perturbations by demanding linear stability. We comment on the possibility of distinguishing this theory from ΛCDM with current and future large-scale structure surveys.
Highlights
Chamseddine and Mukhanov have recently proposed [1,2] a novel ghost-free theory of massive gravity in which one of the four Stückelberg scalars is constrained in the same way as in the mimetic theory of dark matter [3], spontaneously breaking Lorentz invariance
In this Letter we have studied the first cosmological implications of the recently-proposed theory of mimetic massive gravity
We find that the theory is unable to self-accelerate without introducing a ghost
Summary
Chamseddine and Mukhanov have recently proposed [1,2] a novel ghost-free theory of massive gravity in which one of the four Stückelberg scalars is constrained in the same way as in the mimetic theory of dark matter [3], spontaneously breaking Lorentz invariance. I.e., linearizing the metric about flat space in unitary gauge, gμν = ημν + hμν and A = xA , we find that one of the six degrees of freedom leads to a ghost instability unless we arrange the mass term into the Fierz-Pauli form, Lmass ∼ h2μν − h2, in which case the dynamics of the ghostly mode take the form of a total derivative Continuing this procedure at higher orders in perturbation theory—i.e., continually packaging ghostly operators into total derivative structures—leads uniquely to the non-linear massive gravity theory of de Rham, Gabadadze, and Tolley (dRGT) [8,9]. The analogue of the Higuchi bound in Lorentz-violating massive gravity was derived in Ref. [28], and for our values of the mi parameters, it reduces to H2 > 0, which is trivially satisfied
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