Math 2.0

Astronomy and astrophysics Definition

Baryon acoustic oscillations

Builds on Speed of soundRecombinationScale factorGalaxy two-point correlation function

Definition

Before recombination, photons and baryons form a single fluid. Its speed of sound is cs=c3(1+R),R=3ρb4ργ,c_s = \frac{c}{\sqrt{3 (1 + R)}}, \qquad R = \frac{3 \rho_b}{4 \rho_\gamma}, where ρb\rho_b and ργ\rho_\gamma are the densities of baryons and photons. Let a(t)a(t) be the scale factor and tdt_d the time at which baryons decouple from photons (the drag epoch). The sound horizon is the comoving distance rs=∫0tdcs(t)a(t) dt.r_s = \int_0^{t_d} \frac{c_s(t)}{a(t)} \, dt. Baryon acoustic oscillations are the oscillations of the photon-baryon fluid driven by pressure and gravity, together with their imprint on later matter. The imprint is a peak at separation rsr_s in the two-point correlation function of matter and galaxies. Equivalently, it is a series of oscillations in the power spectrum.

Remarks

The measured sound horizon is about 147147 Mpc in comoving units, that is about 100h−1100 h^{-1} Mpc. Because rsr_s is predicted from the physics before decoupling, measuring its apparent size at different redshifts gives distances, a standard ruler.

Example: a single initial point-like overdensity drives a spherical sound shell that moves at speed csc_s until tdt_d. After that the shell stays at comoving radius rsr_s, which is the definition at work. The same oscillations, seen in the photons, give the acoustic peaks of the microwave background.

Non-example: a universe with only cold dark matter, and no baryons coupled to photons, has no pressure acting on the matter. No sound wave runs through the matter, and its correlation function has no peak at a preferred separation.

The peak was first detected in galaxy surveys in 2005.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph
Galaxy two-point correlation function, concept, no evidence levelGalaxy two-point corr…conceptRecombination, concept, no evidence levelRecombinationconceptScale factor, concept, no evidence levelScale factorconceptSpeed of sound, concept, no evidence levelSpeed of soundconceptBaryon acoustic oscillations, definition, no evidence levelBaryon acoustic oscil…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Galaxy two-point correlation function concept
  2. Recombination concept
  3. Scale factor concept
  4. Speed of sound concept
  5. Baryon acoustic oscillations definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations
About this page
Tag8SWMCCYJJJ
URIm2://8SWMCCYJJJ
Kinddefinition
WritingW0 stub
MSC85A40
DefinesBaryon acoustic oscillations
UsesSpeed of sound, Recombination, Scale factor, Galaxy two-point correlation function
Changed3 November 2026

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