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

Abstract

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, $H\ell \gg 1$, where $H$ is the de Sitter expansion rate and $\ell$ is the curvature radius of the AdS bulk. We also show that, in the short distance limit $r\ll \min \{\ell ,H^{-1}\}$, the Brans-Dicke gravity is obtained, whereas in the large distance limit $r\gg \max \{\ell ,H^{-1}\}$, the Brans-Dicke gravity is obtained for $H\ell =O(1)$, and the Einstein gravity is recovered both for $H\ell \gg 1$ and $H\ell \ll 1$. In the limit $H\ell \to 0$, these results smoothly match to the results known for the Minkowski brane.

17 pages, some references added

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