Cosmological Perturbations Generated in the Colliding Bubble Braneworld Universe

TL;DR

This paper analyzes the generation of cosmological perturbations in a colliding bubble braneworld scenario, correcting previous errors and extending the analysis to include bubbles expanding in de Sitter space, with implications for the resulting power spectrum.

Contribution

It provides a linear order calculation of cosmological perturbations in a colliding bubble braneworld, correcting prior claims of scale-invariance and extending the analysis to de Sitter expansion.

Findings

Dominant power spectrum contribution is 'red' in dS5 expansion.

Errors in previous scale-invariance claims are corrected.

Perturbation effects depend on the size of the fifth dimension.

Abstract

We compute the cosmological perturbations generated in the colliding bubble braneworld universe in which bubbles filled with five-dimensional anti-de Sitter space (AdS5)expanding within a five dimensional de Sitter space (dS5) or Minkowski space (M5) collide to form a (3+1) dimensional local brane on which the cosmology is virtually identical to that of the Randall-Sundrum model. The perturbation calculation presented here is valid to linear order but treats the fluctuations of the expanding bubbles as (3+1) dimensional fields localized on the bubble wall. We find that for bubbles expanding in dS5 the dominant contribution to the power spectrum is `red' but very small except in certain cases where the fifth dimension is not large or the bubbles have expanded to far beyond the dS5 apparent horizon length. This paper supersedes a previous version titled "Exactly Scale-Invariant Cosmological Perturbations From a Colliding Bubble Braneworld Universe" in which we erroneously claimed that a scale-invariant spectrum results for the case of bubbles expanding in M5. This present paper corrects the errors of the previous version and extends the analysis to the more interesting and general case of bubbles expanding in dS5.