Massive Gravity

TL;DR

This work surveys massive gravity as a viable extension of GR, focusing on how gravity can be mediated by a massive spin-2 field while avoiding the Boulware–Deser ghost. It develops several theoretical pathways—extra dimensions (DGP and cascading gravity), deconstruction, and ghost-free nonlinear realizations (dRGT) with multi-gravity and bi-gravity —and analyzes their consistency via ADM, Stückelberg, and vielbein formalisms, including the crucial Λ3 decoupling limit where Galileon interactions emerge. The review also covers key phenomenological aspects, notably the Vainshtein mechanism that screens extra degrees of freedom to recover GR in the solar system, and the cosmological implications such as self-acceleration branches, degravitation ideas, and their observational viability. Finally, it surveys extensions (mass-varying, quasi-dilaton, and partially massless scenarios) and discusses the status and challenges of nonlinear PM gravity, highlighting the ongoing quest for consistent, ghost-free infrared-modified gravity with potential cosmological applications.

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, 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.

Figures (7)

• 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: Codimension-2 brane with positive (resp. negative) tension brane leading to a positive (resp. negative) deficit angle in the two extra dimensions.
• Figure 3: Seven-dimensional cascading scenario and solution for one the metric potential $\Phi$ on the $(5+1)$-dimensional brane in a 7-dimensional Cascading gravity scenario with tension on the $(3+1)$-dimensional brane located at $y=z=0$, in the case where $M_6^4/M_5^3 = M_7^5/M_6^4=m_7$. $y$ and $z$ represent the two extra dimensions on the $(5+1)$-dimensional brane. From deRham:2009wb.
• 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 line $m=0$ corresponding to GR.
• Figure 5: Difference between phase, group, signal and front velocities. At $t=\delta t$, the phase and group velocities are represented on the left and given respectively by $v_{\rm phase}= \delta x_P/\delta t$ and $v_{\rm group}= \delta x_G/\delta t$ (in the limit $\delta t \to 0$.) The signal and front velocity represented on the right are given by $v_{\rm signal}=\delta x_S/\delta t$ (where $\delta x_S$ is the point where at least half the intensity of the original signal is reached.) The front velocity is given by $v_{\rm front}= \delta x_F/\delta t$.