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

TL;DR

This paper studies linearized gravity on a de Sitter brane within Einstein Gauss-Bonnet theory, revealing conditions under which Einstein or Brans-Dicke gravity are recovered at different scales and limits.

Contribution

It provides a detailed analysis of gravity behavior on a de Sitter brane in EGB theory, including the transition between Einstein and Brans-Dicke gravity depending on energy scale and distance.

Findings

Einstein gravity is recovered at high energy branes with large expansion rate.

Brans-Dicke gravity appears at short distances, while Einstein gravity is recovered at large distances for certain parameters.

Results smoothly connect to Minkowski brane case as Hℓ approaches zero.

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 $H\ell\gg1$ and $H\ell\ll1$. In the limit $H\ell\to0$, these results smoothly match to the results known for the Minkowski brane.