Strong cosmic censorship in charged de sitter spacetime with scalar field non-minimally coupled to curvature

We examine the strong cosmic censorship in the Reissner-Nordstrom-de Sitter (RN-dS) black hole by investigating the evolution of a scalar field non-minimally coupled to the curvature. We find that for the stable RN-dS black hole, with the increase of the coupling parameter, the violation of the strong cosmic censorship occurs at a larger critical charge ratio. But such an increase of the critical charge is suppressed by the increase of the cosmological constant. Different from the minimal coupling situation, it is possible to accommodate beta >= 1 in the near extremal black hole when the scalar field is non-minimally coupled to curvature. beta here is defined as beta equivalent to -Im omega/kappa_ where kappa_ is the surface gravity of Cauchy horizon and omega is the frequency of quasinormal modes. The increase of the cosmological constant can allow beta >= 1 to be satisfied for even smaller value of the coupling parameter. The existence of beta >= 1 implies that the resulting curvature can continuously cross the Cauchy horizon.