Brane-world inflation: slow-roll corrections to the spectral index

TL;DR

This paper investigates how slow-roll corrections in brane-world inflation affect the spectral index of primordial density perturbations, confirming that leading-order effects align with previous findings.

Contribution

It provides a detailed quantification of slow-roll corrections to the spectral index in brane-world inflation, validating previous leading-order approximations.

Findings

Late-time perturbation amplitudes differ from classical solutions by first-order slow-roll parameters.

Second-order slow-roll corrections to the spectral index are confirmed.

Leading-order effects match previous theoretical predictions.

Abstract

We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are correctly given by previous work in the literature.