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 anti-de Sitter space (AdS(5)) expanding within a five-dimensional de Sitter space (dS(5)) or Minkowski space (M-5) 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 dS(5) the dominant contribution to the power spectrum is "red," with dP(k)/d[log(k)]approximate to1/(m(4)l)(2)[1+(R/l(ext))(2)](2)(l/R)(2)(k(c)/k)(2) 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 AdS(5) space within the bubbles, l(ext) is the curvature radius of the dS(5) (taken as infinite for the M-5 case), k(c) is the wave number of the spatial curvature scale, and m(4) is the four-dimensional Planck mass. The perturbations are minuscule and well below observational detection except when (m(4)l) is not large or in certain cases where R at the moment of collision exceeds (R) over bar =l(ext)(l(ext)/l).