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, Hl ≫ 1, where H is the de Sitter expansion rate and l is the curvature radius of the AdS bulk. We also show that, in the short distance limit r ≪ min{l, H}, the Brans-Dicke gravity is obtained, whereas in the large distance limit r ≫ max{l, H}, a Brans-Dicke type theory is obtained for Hl = O(1), and the Einstein gravity is recovered both for Hl ≫ 1 and Hl ≪ 1. In the limit Hl → 0, these results smoothly match to the results known for the Minkowski brane.