  Black holes (BHs) exhibiting coordinate singularities but lacking essential
singularities throughout the entire spacetime are referred to as regular black
holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who
considered the Einstein equation coupled with a nonlinear electromagnetic
field. In this study, we investigate the gravitational perturbations, including
the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We
derive the master equations with source terms for both axial and polar
perturbations, and subsequently compute the quasinormal modes (QNMs) through
numerical methods. For the Bardeen de Sitter black hole, we employ the
6th-order WKB approach. The numerical results reveal that the isospectrality is
broken in this case. Conversely, for Bardeen Anti-de Sitter black holes, the
QNM frequencies are calculated by using the HH method.
