Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 310 / 3 / e / Solution

Yes. The baryons carry the oscillatory baryon transfer function inherited from the pre-recombination photon-baryon fluid. Their later infall toward cold-dark-matter overdensities suppresses the relative mode and drives ${\delta }_b/{\delta }_c\to 1$, but gravitational evolution does not remove every scale-dependent acoustic phase. The total cosmological density power spectrum therefore contains the small wiggles known as a baryon acoustic oscillation in the matter power spectrum.