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Large-distance modification of gravity may be the best mechanism for solving the cosmological constant problem. A simple model of the large-distance modification---four-dimensional (4D) gravity with a hard mass term---is problematic from the theoretical standpoint. Here we discuss a different model, brane-induced gravity, that effectively introduces a soft graviton mass. We study the issues of unitarity, analyticity, and causality in this model in more than five dimensions. We show that a consistent prescription for the poles of the Green's function can be specified so that 4D unitarity is preserved. However, in certain instances 4D analyticity cannot be maintained when the theory becomes higher dimensional. As a result, one has to sacrifice 4D causality at distances of the order of the present-day Hubble scale. This is a welcome feature for solving the cosmological constant problem, as was recently argued in the literature. We also show that, unlike 4D massive gravity, the model has no strong-coupling problem at intermediate scales.
Gabadadze et al. (Tue,) studied this question.