Scalar cosmological perturbations in the Gauss-Bonnet braneworld

TL;DR

This paper analyzes scalar cosmological perturbations in a Gauss-Bonnet braneworld, demonstrating how perturbation equations behave across different energy regimes and confirming the validity of four-dimensional gravity and Brans-Dicke theory limits.

Contribution

It derives boundary conditions for perturbations in a Gauss-Bonnet braneworld and explores the behavior of perturbations in low, high, and intermediate energy limits, including the form of the Sasaki-Mukhanov equation.

Findings

Reproduces four-dimensional Einstein gravity at low energies.

Shows perturbation dynamics follow Brans-Dicke theory on small scales.

Confirms the Sasaki-Mukhanov equation holds at high energies for inflation models.

Abstract

We study scalar cosmological perturbations in a braneworld model with a bulk Gauss-Bonnet term. For an anti-de Sitter bulk, the five-dimensional perturbation equations share the same form as in the Randall-Sundrum model, which allows us to obtain metric perturbations in terms of a master variable. We derive the boundary conditions for the master variable from the generalized junction conditions on the brane. We then investigate several limiting cases in which the junction equations are reduced to a feasible level. In the low energy limit, we confirm that the standard result of four-dimensional Einstein gravity is reproduced on large scales, whereas on small scales we find that the perturbation dynamics is described by the four-dimensional Brans-Dicke theory. In the high energy limit, all the non-local contributions drop off from the junction 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-Mukhanov equation holds on the high energy brane in its original four-dimensional form.