Massive scalar field perturbations of 4D de Sitter Einstein-Gauss-Bonnet black holes

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 non-perturbative (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 non-perturbative dS branch of modes, absent when $\alpha=0$, emerges as a novel feature of the Einstein-Gauss-Bonnet framework.