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In the scope of the nonlinear massive gravity, we study fixed points of evolution equations for a Bianchi type–I universe. We find a new attractor solution with non-vanishing anisotropy, on which the physical metric is isotropic but the Stuckelberg configuration is anisotropic. As a result, at the background level, the solution describes a homogeneous and isotropic universe, while a statistical anisotropy is expected from perturbations, suppressed by smallness of the graviton mass.

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