Cosmological perturbations from braneworld inflation with a Gauss-Bonnet term

TL;DR

This paper investigates how the inclusion of a Gauss-Bonnet term in braneworld inflation models affects the amplitude of cosmological perturbations, revealing modifications to gravitational wave amplitudes and the tensor-to-scalar ratio.

Contribution

It provides an exact analysis of tensor perturbations with a Gauss-Bonnet term, showing how it alters the amplitude and the consistency relation in braneworld inflation.

Findings

Tensor perturbations satisfy the same wave equation as in Randall-Sundrum but with modified amplitude.

Amplitude of gravitational waves decreases asymptotically after an initial rise at high energies.

Tensor-to-scalar ratio breaks the standard consistency relation due to Gauss-Bonnet effects.

Abstract

Braneworld inflation is a phenomenology related to string theory that describes high-energy modifications to general relativistic inflation. The observable universe is a braneworld embedded in 5-dimensional anti de Sitter spacetime. Whe the 5-dimensional action is Einstein-Hilbert, we have a Randall-Sundrum type braneworld. The amplitude of tensor and scalar perturbations from inflation is strongly increased relative to the standard results, although the ratio of tensor to scalar amplitudes still obeys the standard consistency relation. If a Gauss-Bonnet term is included in the action, as a high-energy correction motivated by string theory, we show that there are important changes to the Randall-Sundrum case. We give an exact analysis of the tensor perturbations. They satisfy the same wave equation and have the same spectrum as in the Randall-Sundrum case, but the Gauss-Bonnet change to the junction conditions leads to a modified amplitude of gravitational waves. The amplitude is no longer monotonically increasing with energy scale, but decreases asymptotically after an initial rise above the standard level. Using an approximation that neglects bulk effects, we show that the amplitude of scalar perturbations has a qualitatively similar behaviour to the tensor amplitude. In addition, the tensor to scalar ratio breaks the standard consistency relation.