Cosmological Perturbations Generated in the Colliding Bubble Braneworld Universe

We compute the cosmological perturbations generated in the colliding bubble braneworld universe in which bubbles filled with five-dimensional antide 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 RandallSundrum 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’, with dP (k)/d[log(k)] ≈ 1/(m4l)[1+ (R/lext)](l/R)(kc/k) where R is the spatial curvature radius of the universe on the local brane at the moment of bubble collision, l is the curvature radius of the bulk AdS5 space within the bubbles, lext is the curvature radius of the dS 5 (taken as infinite for the M5 case), kc is the wavenumber of the spatial curvature scale, and m4 is the four-dimensional Planck mass. The perturbations are minuscule and well below observational detection except when (m4l) is not large or in certain cases where R at the moment of collision exceeds R̄ = lext(lext/l). Note: 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 paper corrects the errors of the previous version and extends the analysis to the more interesting and general case of bubbles expanding in dS5. ∗E-mail: [email protected] †E-mail: [email protected]