Gravitational wave speed: Implications for models without a mass scale

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The recent report that the gravitational wave speed equals the light speed puts strong constraints on the anisotropic stress parameter of many modified gravity models, a quantity that is directly observable through large-scale structure. We show here that models without a mass scale completely escape these constraints. We discuss a few relevant cases in detail: Brans-Dicke theory, nonlocal models, and Galileon Lagrangian.