Behavior of Cosmological Perturbations in the Brane-World Mode

TL;DR

This paper develops a gauge-invariant formalism to analyze scalar cosmological perturbations in a brane-world model, revealing that late-time behavior matches standard cosmology, but early universe perturbations differ significantly.

Contribution

It introduces a new gauge-invariant formalism for brane-world perturbations and analyzes their behavior, highlighting differences from standard cosmology in the early universe.

Findings

Late-time superhorizon perturbations behave like standard cosmology.

Early universe perturbations in brane-world differ from standard models.

Conservation of the Bardeen parameter does not hold in the brane-world early universe.

Abstract

In this paper we present a gauge-invariant formalism for perturbations of the brane-world model developed by the author, A. Ishibashi and O. Seto recently, and analyze the behavior of cosmological perturbations in a spatially flat expanding universe realized as a boundary 3-brane in AdS$^5$ in terms of this formalism. For simplicity we restrict arguments to scalar perturbations. We show that the behavior of cosmological perturbations on superhorizon scales in the brane-world model is the same as that in the standard no-extradimension model, irrespective of the initial condition for bulk perturbations, in the late stage when the cosmic expansion rate $H$ is smaller than the inverse of the bulk curvature scale $\ell$. Further, we give rough estimates which indicate that in the early universe when $H$ is much larger than $1/\ell$, perturbations in these two models behave quite differently, and the conservation of the Bardeen parameter does not hold for superhorizon perturbations in the brane-world model.