In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms (the epoch of recombination), which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler (≈490 million light years in today's universe) can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy (which causes the accelerating expansion of the universe) by constraining cosmological parameters.
The early universe
The early universe consisted of a hot, dense plasma of electrons and baryons (which include protons and neutrons). Photons (light particles) traveling in this universe were essentially trapped, unable to travel for any considerable distance before interacting with the plasma via Thomson scattering. The average distance which a photon could travel before interacting with the plasma is known as the mean free path of the photon. As the universe expanded, the plasma cooled to below 3000 K—a low enough energy such that the electrons and protons in the plasma could combine to form neutral hydrogen atoms. This recombination happened when the universe was around 379,000 years old, or at a redshift of . Photons interact to a much lesser degree with neutral matter, and therefore at recombination the universe became transparent to photons, allowing them to decouple from the matter and free-stream through the universe. The cosmic microwave background (CMB) radiation is light that was emitted after recombination, now we see it with our telescopes as radio waves all over the sky since it is red-shifted. Therefore, looking at, for example, Wilkinson Microwave Anisotropy Probe (WMAP) data, one is basically looking back in time to see an image of the universe when it was only 379,000 years old.
WMAP indicates (Figure 1) a smooth, homogeneous universe with density anisotropies of 10 parts per million. However, there are large structures and density fluctuations in the present universe. Galaxies, for instance, are a million times more dense than the universe's mean density. The current belief is that the universe was built in a bottom-up fashion, meaning that the small anisotropies of the early universe acted as gravitational seeds for the structure observed today. Overdense regions attract more matter, whereas underdense regions attract less, and thus these small anisotropies, seen in the CMB, became the large scale structures in the universe today.
Cosmic sound
Imagine an overdense region of the primordial plasma. While this region of overdensity gravitationally attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward pressure. These counteracting forces of gravity and pressure created oscillations, comparable to sound waves created in air by pressure differences.
This overdense region contains dark matter, baryons and photons. The pressure results in spherical sound waves of both baryons and photons moving with a speed slightly over half the speed of light outwards from the overdensity. The dark matter interacts only gravitationally, and so it stays at the center of the sound wave, the origin of the overdensity. Before decoupling, the photons and baryons moved outwards together. After decoupling the photons were no longer interacting with the baryonic matter and they diffused away. That relieved the pressure on the system, leaving behind shells of baryonic matter. Out of all those shells, representing different sound waves wavelengths, the resonant shell corresponds to the first one as it is that shell that travels the same distance for all overdensities before decoupling. This radius is often referred to as the sound horizon. Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons was gravitational. Therefore, the baryons and dark matter (left behind at the center of the perturbation) formed a configuration which included overdensities of matter both at the original site of the anisotropy and in the shell at the sound horizon for that anisotropy.