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We study anisotropic deformations of the spatially open homogeneous andisotropic cosmology in the ghost free massive gravity theory with flatreference metric. We find that if the initial perturbations are not too strongthen the physical metric relaxes back to the isotropic de Sitter state.However, the dumping of the anisotropies is achieved at the expense of excitingthe Stueckelberg fields in such a way that the reference metric changes anddoes not share anymore with the physical metric the same rotational andtranslational symmetries. As a result, the universe evolves towards a fixedpoint which does not coincide with the original solution, but for which thephysical metric is still de Sitter. If the initial perturbation is strong, thenits evolution generically leads to a singular anisotropic state or, for someparameter values, to a decay into flat spacetime. We also present an infinitedimensional family of new homogeneous and isotropic cosmologies in the theory.

Anisotropic deformations of spatially open cosmology in massive gravity theory