Baryon Acoustic Oscillations (BAO) are fluctuations in the density of Baryons (i.e., matter) that stem from acoustic waves in the Early Universe. They provide a means of determining distances and sizes of observed structures in the universe. The oscillations are found by analyzing large amounts of Survey data. The expected signature is Galaxy pairs 150 million Parsecs apart where there is expected an Acoustic Peak in matter density. This is a proposed Standard Ruler, i.e., distance that can be determined by observation, useful for future studies. This characteristic of galaxy location would not be significantly affected by subsequent movement of the matter, which is in the range of 3 to 10 Mpc. Through study of the early universe, the standard ruler can be determined within 1%.
The oscillations stem from Inflation causing early-universe density perturbations before Recombination, when matter was nearly all protons, which continually scattered Photons via Thomson Scattering in effect forming a gas (Plasma) with pressure counteracting the Gravity. Dense regions released expanding sound waves, and from study of the Cosmic Microwave Background, it is determined these result in the above-mentioned acoustic peak at the time of recombination, when the ionized Hydrogen was neutralized (captured electrons), thus became transparent, no longer scattering photons so readily, so photons no longer contributed to a pressure as before, and the baryons (hydrogen) remained as left by the characteristic sound waves.
The BAO signal has been detected in the Sloan Digital Sky Survey data.