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The covariant St\"{u}ckelberg formalism is applied to bi-gravity in order torevisit the issue of absence of the Boulware-Deser (BD) ghost. We first confirmthat the leading order action in the decoupling limit for helicity-2 modes ofmetrics and helicity-0 mode of St\"{u}ckelberg perturbations does not lead tohigher time derivative in equations of motion, which suggests the absence ofthe BD ghost. By extending this method, we reconfirm that the BD ghost does notappear for arbitrary order of the perturbations at the decoupling limit inbi-gravity.

Note on Covariant St\"uckelberg Formalism and Absence of Boulware-Deser Ghost in Bi-gravity