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The regularization proposed in [D.~Glavan and C.~Lin, Phys.\ Rev.\ Lett.\{\bf 124}, 081301 (2020)] led to the black hole solutions which turned out tobe the solutions of the consistent well-defined $4$-dimensionalEinstein-Gauss-Bonnet theory of gravity suggested in [K.~Aoki, M.~Gorji andS.~Mukohyama, arXiv:2005.03859]. Recently the quasinormal modes of bosonic andfermionic fields for this theory were studied. Here we calculate quasinormalfrequencies of the test scalar, electromagnetic and Dirac fields for thespherically symmetric black hole in the novel $4D$ Einstein-Gauss-Bonnet-deSitter theory. The values of the quasinormal modes, calculated by the sixthorder WKB method with Pad\'{e} approximants and the time-domain integration,show that both real oscillation frequency and the damping rate are suppressedby increasing of the cosmological constant. While the stability of the scalarand electromagnetic fields follows directly from the positive definiteness ofthe effective potential, there is no such positive definiteness for the Diracfield. Here, with the help of the time domain integration, taking into accountall the modes, we prove stability of the Dirac field in $4D$Einstein-Gauss-Bonnet-de Sitter theory.

Quasinormal modes of the test fields in the novel 4D Einstein-Gauss-Bonnet-de Sitter gravity