Linearized gravity on the de Sitter brane in the Einstein Gauss-Bonnet theory

We investigate the linearized gravity on a single de Sitter brane in the anti-de Sitter (AdS) bulk in the Einstein Gauss-Bonnet (EGB) theory. We find that the Einstein gravity is recovered for a high energy brane, i.e., in the limit of the large expansion rate, $H\mathrm{\ell }\gg 1$, where $H$ is the de Sitter expansion rate and $\mathrm{\ell }$ is the curvature radius of the AdS bulk. We also show that, in the short distance limit $r\ll \min \{\mathrm{\ell },H^{-1}\}$, the Brans-Dicke gravity is obtained, whereas in the large distance limit $r\gg \max \{\mathrm{\ell },H^{-1}\}$, the Brans-Dicke gravity is obtained for $H\mathrm{\ell }=O(1)$, and the Einstein gravity is recovered both for $H\mathrm{\ell }\gg 1$ and $H\mathrm{\ell }\ll 1$. In the limit $H\mathrm{\ell }\to 0$, these results smoothly match to the results known for the Minkowski brane.