Cosmological and astrophysical Vainshtein mechanism in bigravity

Although the linear massive spin-2 theory is not restored to general relativity (GR) even in a massless limit, Vainshtein proposed the discontinuity can be resolved by taking into account nonlinear interactions. We consider whether the nonlinear ghost-free bigravity theory can be restored to GR both in the cosmological background and in the strong gravitational field based on a spherically symmetric configuration. In the cosmological background, the scalar graviton is stabilized by nonlinear interactions in the early stage of the Universe, thus the bigravity has the GR limit with neither a ghost instability nor a gradient instability. On the other hand, the bigravity cannot describe a static compact object beyond a critical value of gravitational field strength for a parameter space of coupling constants, at which the scalar graviton shows a singular behaviour.