The sub-sub-leading order soft graviton theorem has previously been derived from an explicit calculation amplitudes (1404.4091), and here it is argued that it follows as a consequence of new asymptotic symmetries at null infinity. In previous work, the Christodoulou-Klainerman (CK) condition has been used to relate the positive and negative helicity soft theorems; however, this condition corresponds to setting the magnetic charge to zero. Relaxing the CK condition, one finds two charges for each supertranslation, analogous to electric and magnetic charges in QED. The sub-sub-leading graviton theorem is conjectured to follow from the `magnetic' charge associated to the dual of the Weyl tensor. (Here they consider linearized gravity coupled to a massless scalar field, and derive the `magnetic charge' starting from the desired soft theorem. Although the corresponding asymptotic symmetry is roughly outlined - a more rigorous analysis is left for future work.)

Recently, the connection between the asymptotic symmetries and soft theorems has been illustrated in a number of interesting cases. For example, the BMS group of supertranslations in asymptotically flat spacetimes gives the leading soft graviton theorem (and superrotations give the sub-leading order). Here this program is extended to the sub-sub-leading soft graviton theorem, and highlights the role that `magnetic' charges play in gravitational theories. Also, the vector field symmetries discussed here do not form a group, so it's not clear that they share previous interpretations of asymptotic symmetries as maps between degenerate vacua at the boundary.

Using a previous 5D framework, in which the physical metric lives on the conformal boundary of AdS₅, one can describe dRGT massive gravity (in such a way that that fiducial metric is determined by the pullback of the metric in the bulk). Ordinarily, in the 4D construction of massive gravity, total derivative terms of the helicity-0 mode in the decoupling limit are ignored. But in this 5D construction, one should retain them, as they contribute nonlocal boundary terms to the helicity-2 equations of motion. These corrections affect the stability properties of self-accelerating, cosmologically viable solutions. (Calculations are carried out in the decoupling limit, and therefore valid at scales smaller than the Hubble scale.)

Modelling our presently accelerating Universe using massive gravity is an appealing alternative to GR with a cosmological constant - for one thing, a graviton mass can remain small on including quantum corrections. However, generally small fluctuations about self-accelerating solutions in massive gravity can be unstable, and exhibit superluminal propagation. Here, it is shown how the addition of nonlocal terms can give rise to stable self-accelerating solutions in massive gravity, which may describe our current Universe.