We investigate the propagation of massive scalar fields in the background of four-dimensional Einstein-Gauss-Bonnet black holes with de Sitter (dS) asymptotics. Our study focuses on the various branches of quasinormal modes present in this background, employing the pseudospectral Chebyshev method and the third-order Wentzel-Kramers-Brillouin approximation. We identify that the introduction of the Gauss-Bonnet coupling constant $\alpha$ gives rise to three branches of modes: the perturbative (in $\alpha$) Schwarzschild branch, the perturbative (in $\alpha$) dS branch, and a nonperturbative (in $\alpha$) dS branch. Our results show that the propagation of a massive scalar field is stable in this background. Furthermore, the Gauss-Bonnet coupling constant induces significant deviations in the Schwarzschild branch and smaller deviations in the perturbative dS branch compared to the corresponding branches in the Schwarzschild-dS limit. Additionally, the nonperturbative dS branch of modes, absent when $\alpha =0$, emerges as a novel feature of the Einstein-Gauss-Bonnet framework.

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• Alternative gravity theories
• Classical black holes
• General relativity equations & solutions
• General relativity formalism