Extreme parameter sensitivity in quasidilaton massive gravity

We reanalyze the behavior of Friedmann-Lema\^itre-Robertson-Walker cosmologies in the recently proposed quasidilaton massive-gravity model, and discover that the background dynamics present hitherto unreported features that require unexpected fine-tuning of the additional fundamental parameters of the theory for an observationally consistent background cosmology. We also identify new allowed regions in the parameters space and exclude some of the previously considered ones. The evolution of the mass of gravitational waves reveals non-trivial behavior, exhibiting a mass squared that may be negative in the past, and that presently, while positive, is larger than the square of the Hubble parameter. These properties of the gravity-wave mass have the potential to lead to observational tests of the theory. While quasidilaton massive gravity is known to have issues with stability at short distances, the current analysis is a first step toward the investigation of the more stable extended quasidilaton massive gravity theory, with some expectation that both the fine-tuning of parameters and the interesting behavior of the gravity-wave mass will persist.