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Bigravity is one of the natural extensions of general relativity and contains an additional massive spin-2 field which can be a good candidate for dark matter. To discuss the production of spin-2 dark matter, we study fixed-point solutions of the background equations for axisymmetric Bianchi type-I universes in two bigravity theories without a Boulware-Deser ghost, i.e., Hassan-Rosen bigravity and the minimal theory of bigravity. We investigate the local and global stabilities of the fixed points and classify them. Based on the general analysis, we propose a new scenario where spin-2 dark matter is produced by the transition from an anisotropic fixed-point solution to an isotropic one. The produced spin-2 dark matter can account for all or a part of dark matter and can be directly detected by laser interferometers in the same way as gravitational waves.
Manita et al. (Tue,) studied this question.