Deconstructing dimensions and massive gravity

Abstract

Abstract. We show that the ghost-free models of massive gravity and their multigraviton extensions follow from considering higher dimensional General Relativity in Einstein-Cartan form on a discrete extra dimension, according to the Dimensional Deconstruction paradigm. We show that Dimensional Deconstruction is equivalent to a truncation of the Kaluza-Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza-Klein tower) due to the appearance of a low strong coupling scale that depends on IR physics. This strong coupling scale, which is associated with the mass of the lowest Kaluza-Klein mode, controls the onset of the Vainshtein mechanism and is crucial to the theoretical and observational viability of the truncated theory.

Renormalizable toy model of massive spin-two field and new bigravity

“…In [39], however, it has been shown that the non-linear terms (10) and (11) could generate the ghost by using the mini-superspace where…”

“…Then we consider the possibility of other classes of the no-ghost interactions by relaxing the assumption in [39]. In the argument so far, we have considered the terms which have invariance under the general coordinate transformation if the fiducial metric f µν could be a dynamical tensor.…”

“…Anyway we may consider deformation similar to (39) of the model by adding the following new term to the Lagrangian density (32):…”

“…Recently in [36], it has been proposed possibilities of new non-linear ghost-free derivative interactions in massive gravity. After that, however, in [39], it has shown that a class of the derivative interactions includes ghost and a kind of no-go theorem prohibiting the derivative interactions has been claimed. In this paper, we show the existence of the non-linear derivative interactions which are not included in [39] although such derivative interactions generate ghost, unfortunately.…”

The nature of spacetime in bigravity: Two metrics or none?

“…Firstly, the structure of the viable bigravity action is symmetric under exchange of the two metrics. We also note that one could arrive at the double minimal coupling from extra-dimensional constructions [14] attempting to obtain bigravity as the low-energy limit. However, it was very recently shown [15,16] that minimally coupling matter to each metric separately, which is the case we consider here, revives the Boulware-Deser ghost [17].…”