Towards construction of ghost-free higher derivative gravity from bigravity

In this paper, the ghost-freeness of the higher derivative theory proposed by Hassan et al. in [Universe 1 (2015) 2, 92] is investigated. Hassan et al. believed the ghost-freeness of the higher derivative theory based on the analysis in the linear approximation. However, in order to obtain the complete correspondence, we have to analyze the model without any approximations. In this paper, we analyze two scalar model proposed in [Universe 1 (2015) 2, 92] with arbitrary nonderivative interaction terms. In any order with respect to perturbative parameter, we prove that we can eliminate the ghost for the model with any nonderivative interaction terms.