It was recently shown that only a finite region of parameter space in dRGT massive gravity is capable of admitting a unitary, analytic UV completion. This paper considers a pp-wave background (written in Kerr-Schild form), and shows that there can be a signal time advance which is within the EFT regime of validity, unless the dRGT parameter α₃=-1/2. They argue that this implies the existence of closed time-like curves, and therefore that one should further restrict the dRGT parameter space to this line.

The low energy effective description of dRGT massive gravity involves only two free parameters once one imposes the required symmetries and classical ghost freedom. By demanding additional properties of the theory, one can constraint these free parameters, which is useful for future phenomenological investigations (as then only a finite region of parameter space needs to be tested against observation in order to rule the theory out). The additional property demanded here is the absence of closed time-like curves on a particular non-trivial background. However, while the authors succeed in showing that there is a resolvable time advance, this a weaker observation than closed time-like curves. Also, the background itself saturates the Null Energy Condition, is not asymptotically flat, and contains a singularity, and so is not very physical. One may then wonder whether we should take the existence of these time advances as particulary dangerous for the theory.