Baryon acoustic oscillations are the relic spatial scale of sound waves in the pre-recombination photon-baryon fluid. The scale appears both as a preferred separation in galaxy clustering and as oscillatory structure in the cosmological density power spectrum.
The epoch at which momentum exchange with photons ceases to drag baryons efficiently. The sound horizon at this epoch calibrates the late-time baryon acoustic oscillation ruler. It is related to, but not identical with, photon last scattering.
For a comoving BAO scale perpendicular to the line of sight in a spatially flat universe,
Its redshift dependence constrains the shape of the distance--redshift relation.
For a small comoving BAO separation parallel to the line of sight,
in units with . Combining this with a transverse measurement eliminates the unknown ruler size.
The matter power spectrum contains low-amplitude oscillatory features because baryons preserve their pre-recombination acoustic phase and later transfer part of it gravitationally to the combined matter distribution.

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