  We study the evolution of cosmological perturbations in an anti-de-Sitter
(AdS) bulk through a cosmological singularity by mapping the dynamics onto the
boundary conformal fields theory by means of the AdS/CFT correspondence. We
consider a deformed AdS space-time obtained by considering a time-dependent
dilaton which induces a curvature singularity in the bulk at a time which we
call $t = 0$, and which asymptotically approaches AdS both for large positive
and negative times. The boundary field theory becomes free when the bulk
curvature goes to infinity. Hence, the evolution of the fluctuations is under
better controle on the boundary than in the bulk. To avoid unbounded particle
production across the bounce it is necessary to smooth out the curvature
singularity at very high curvatures. We show how the bulk cosmological
perturbations can be mapped onto boundary gauge field fluctuations. We evolve
the latter and compare the spectrum of fluctuations on the infrared scales
relevant for cosmological observations before and after the bounce point. We
find that the index of the power spectrum of fluctuations is the same before
and after the bounce.
