Theoretical aspects of massive gravity

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the van Dam, Veltman, and Zakharov (vDVZ) discontinuity and the Boulware-Deser ghost were uncovered. These results are rederived in a pedagogical manner and the Stückelberg formalism to discuss them from the modern effective field theory viewpoint is developed. Recent progress of the last decade is reviewed, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra dimensions and brane worlds are reviewed.

Figure 1

Regimes for massive gravity with cutoff ${\Lambda }_5=(M_P{m}^4{)}^{1/5}$, and some values within the Solar System (i.e., $M$ is the solar mass and $m$ is taken to be the Hubble scale), for which ${\Lambda }_5^{-1}\sim {10}^{11}\mathrm{km}$. Note that $r_Q$ is a bit larger than the observable universe, i.e., this theory makes no observable predictions within its range of validity.

Figure 2

Regimes for massive gravity with cutoff ${\Lambda }_3=(M_P{m}^2{)}^{1/3}$ (i.e., $M$ is the solar mass and $m$ is taken to be the Hubble scale) and some values within the Solar System. The values are much more reasonable than those of the ${\Lambda }_5$ theory.

Figure 3

Splitting the DGP action.