Scalar cosmological perturbations in the Gauss–Bonnet braneworld

Abstract

We study scalar cosmological perturbations in a braneworld model with a bulkGauss–Bonnet term. For an anti-de Sitter bulk, the five-dimensional perturbation equationsshare the same form as in the Randall–Sundrum model, which allows us to obtain metricperturbations in terms of a master variable. We derive the boundary conditions for themaster variable from the generalized junction conditions on the brane. We then investigateseveral limiting cases in which the junction equations are reduced to a feasible level. Inthe low energy limit, we confirm that the standard result of four-dimensionalEinstein gravity is reproduced on large scales, whereas on small scales we find thatthe perturbation dynamics is described by the four-dimensional Brans–Dicketheory. In the high energy limit, all the non-local contributions drop off from thejunction equations, leaving a closed system of equations on the brane. We show that,for inflation models driven by a scalar field on the brane, the Sasaki–Mukhanovequation holds on the high energy brane in its original four-dimensional form.