Baryon acoustic oscillation (BAO)

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.

For a comoving BAO scale ${\chi }_d$ 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 $c=1$. 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.