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

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 to be the solutions of the consistent well-defined $4$-dimensional Einstein-Gauss-Bonnet theory of gravity suggested in [K.~Aoki, M.~Gorji and S.~Mukohyama, arXiv:2005.03859]. Recently the quasinormal modes of bosonic and fermionic fields for this theory were studied. Here we calculate quasinormal frequencies of the test scalar, electromagnetic and Dirac fields for the spherically symmetric black hole in the novel $4D$ Einstein-Gauss-Bonnet-de Sitter theory. The values of the quasinormal modes, calculated by the sixth order WKB method with Pad\'{e} approximants and the time-domain integration, show that both real oscillation frequency and the damping rate are suppressed by increasing of the cosmological constant. While the stability of the scalar and electromagnetic fields follows directly from the positive definiteness of the effective potential, there is no such positive definiteness for the Dirac field. Here, with the help of the time domain integration, taking into account all the modes, we prove stability of the Dirac field in $4D$ Einstein-Gauss-Bonnet-de Sitter theory.