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Review
.2014;17(1):7.
doi: 10.12942/lrr-2014-7. Epub 2014 Aug 25.

Massive Gravity

Affiliations
Review

Massive Gravity

Claudia de Rham. Living Rev Relativ.2014.

Abstract

We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.

Keywords: Alternative theories of gravity; General relativity; Gravity; Massive gravity; Modified theories of gravity.

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Figures

Figure 1
Figure 1
Spectral representation of different models. (a) DGP (b) higher-dimensional cascading gravity and (c) multi-gravity. Bi-gravity is the special case of multi-gravity with one massless mode and one massive mode. Massive gravity is the special case where only one massive mode couples to the rest of the standard model and the other modes decouple. (a) and (b) are models of soft massive gravity where the graviton mass can be thought of as a resonance.
Figure 2
Figure 2
Codimension-2 brane with positive (resp. negative) tension brane leading to a positive (resp. negative) deficit angle in the two extra dimensions.
Figure 3
Figure 3
Seven-dimensional cascading scenario and solution for one the metric potential F on the (5+1)-dimensional brane in a 7-dimensional cascading gravity scenario with tension on the (3 + 1)-dimensional brane located aty =z = 0, in the case whereformula image.y andz represent the two extra dimensions on the (5 + 1)-dimensional brane. Image reproduced with permission from [149], copyright APS.
Figure 4
Figure 4
Degrees of freedom for massive gravity on a maximally symmetric reference metric. The only theoretically allowed regions are the upper left green region and the linem = 0 corresponding to GR.
Figure 5
Figure 5
Difference between phase, group, signal and front velocities. Att =δt, the phase and group velocities are represented on the left and given respectively byv phase =δxP/δt andformula image (in the limitδt → 0.) The signal and front velocity represented on the right are given byvsignal =δxS/δt (whereδxS is the point where at least half the intensity of the original signal is reached.) The front velocity is given byvfront =δxF/δt.
Figure 6
Figure 6
Polarizations of gravitational waves in general relativity and potential additional polarizations in modified gravity.
Figure 7
Figure 7
Alternative ways in deriving the cosmology in massive gravity.
See this image and copyright information in PMC

References

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