Baryon acoustic oscillations are periodic fluctuations in the density of visible matter, serving as a standard ruler for measuring cosmic expansion.Baryon acoustic oscillations are periodic density perturbations of baryonic matter in the early Universe, generated by acoustic waves in the photon-baryon plasma before recombination. The waves had a certain maximum length — the acoustic horizon (about 150 Mpc in current units), which after recombination became a standard ruler. In galaxy distribution, this manifests as a slight increase in the probability of finding two galaxies at a separation of ~150 Mpc. By measuring this scale at different epochs, cosmologists refine the parameters of the Universe's expansion and dark energy.
The concept of sound waves in prestellar matter dates back to work by Evgeny Lifshitz (1946) on gravitational instability. In the 1970s, Jim Peebles and Yuri Zeldovich predicted that these waves would leave an observable trace. The first convincing detection of the BAO peak was made in 2005 by the SDSS collaboration using a sample of red galaxies. Research on nucleosynthesis by George Gamow and Ralph Alpher played a key role in determining the composition of the primordial plasma, which allowed calculation of oscillation parameters.
Before recombination, baryons and photons are tightly coupled by scattering. Gravitational potentials of dark matter attract the baryon-photon fluid; compression increases photon pressure, causing a rebound — this is an acoustic wave. Its speed is determined by the density ratio of baryons to photons: c_s = c / sqrt(3(1+R)), where R = 3ρ_b/4ρ_γ ≈ 0.6 at recombination. By the time of deionization, different oscillation modes freeze in various phases, creating a series of peaks in the power spectrum. The dominant peak corresponds to the wave that traveled a distance r_s ≈ ∫ c_s dt / a(t) from the Big Bang to recombination. Today this scale is seen as a preferred distance between galaxies. Measuring the BAO peak in radial and transverse directions yields the Hubble parameter H(z) and angular diameter distance D_A(z), which is critically important for testing dark energy models.
Serve as a standard ruler for measuring cosmic distances and the expansion rate of the Universe, helping to uncover the nature of dark energy.
The speed of sound in the primordial plasma reached 57% of the speed of light — faster than any modern sound in matter.
| H | variable | Hubble parameter — hubble parameter per second |
| m_a | variable | Axion mass — mass kilogram |
| \theta_{a,0} | variable | Amplitude of polarization oscillation — angle radian |
| g_{a\gamma} | variable | Axion-photon coupling constant — coupling constant reciprocal gev |
| \rho | variable | Local axion dark matter density — mass density kilogram per cubic metre |
| \mu | variable | Axion mass — mass kilogram |
| g(ω) | variable | vibrational density of states — density of states second per radian |
| ω | variable | angular frequency — angular frequency radian per second |
| T | variable | temperature — temperature kelvin |
| ħ | constant | Reduced Planck constant, quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second |
| k | constant | Relates energy to temperature in statistical mechanics — boltzmann constant = 1.380649e-23 joule per kelvin |
| alpha_parallel | variable | BAO scale distortion parameter along line-of-sight — dimensionless parameter |
| H_fid | variable | fiducial Hubble parameter — hubble parameter metre per second per metre |
| r_d_fid | variable | fiducial sound horizon at drag epoch — length metre |
| H | variable | true Hubble parameter — hubble parameter metre per second per metre |
| r_d | variable | true sound horizon at drag epoch — length metre |
| ω | variable | angular frequency — angular frequency radian per second |
| k | variable | spring constant — spring constant newton per metre |
| m | variable | mass — mass kilogram |
| A | variable | amplitude — amplitude metre |
| E | variable | total energy — energy joule |
| √ | operator | square root operation — square root |













