De Sitter brane-world solution in 5-dimensional Einstein-Gauss-Bonnet gravity (Q2226088)

In this paper a new cosmological solution to the five-dimensional Einstein gravity modified with the Gauss-Bonnet term is obtained. The Gauss-Bonnet term is the unique combination in five dimensions that results in second order field equations and is given in terms of the squares of the Ricci scalar, the Ricci tensor and the Riemann tensor. The metric ansatz of the solution is inspired by the braneworld cosmology models which attracted a lot of attention in recent years. In these models, the observable universe is a four dimensional hypersurface (brane) embedded in a higher dimensional spacetime. Here, the induced metric on the brane is chosen as the flat Friedmann-Lemaitre-Robertson-Walker spacetime. As for the energy momentum tensor, it is assumed that five dimensional bulk spacetime is empty and the brane contributes as dust whose effect becomes negligible in an expanding universe. Then, it is shown that under these conditions the four dimensional part is described by the de Sitter geometry.