concept

baryon acoustic oscillations

Baryon acoustic oscillations are periodic fluctuations in the density of visible matter, serving as a standard ruler for measuring cosmic expansion.
29 related articles · 5 formulas · 2 who worked here

Description

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.

History

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.

How it works

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.

In practice

Serve as a standard ruler for measuring cosmic distances and the expansion rate of the Universe, helping to uncover the nature of dark energy.

Fun fact

The speed of sound in the primordial plasma reached 57% of the speed of light — faster than any modern sound in matter.

Concept graph →

Formulas

$$H \approx m_a$$
Axion field oscillates when Hubble rate equals mass.
What is in the formula
HvariableHubble parameter — hubble parameter per second
m_avariableAxion mass — mass kilogram
h(t_{\rmosc})\approxm_a · 2607.01333v1
$$\theta_{a,0} = \frac{g_{a\gamma}}{2} \frac{\sqrt{2\rho}}{\mu}$$
Amplitude of axion-induced polarization oscillations.
What is in the formula
\theta_{a,0}variableAmplitude of polarization oscillation — angle radian
g_{a\gamma}variableAxion-photon coupling constant — coupling constant reciprocal gev
\rhovariableLocal axion dark matter density — mass density kilogram per cubic metre
\muvariableAxion mass — mass kilogram
θ_{a,0}=\frac{g_{aγ}}{2}\frac{\sqrt{2ρ}}{μ} · 2607.04550v1
$$g(\omega) \propto \frac{\omega^3}{e^{\hbar\omega/kT} - 1}$$
Describes the universal low-frequency scaling of vibrational modes in glasses.
What is in the formula
g(ω)variablevibrational density of states — density of states second per radian
ωvariableangular frequency — angular frequency radian per second
Tvariabletemperature — temperature kelvin
ħconstantReduced Planck constant, quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second
kconstantRelates energy to temperature in statistical mechanics — boltzmann constant = 1.380649e-23 joule per kelvin
\frac{g_q(ν)}{ν^2}=\frac{φν^3}{e^{\ellν}-1} · 2607.14764
$$\alpha_\parallel = \frac{H^{\rm fid} r_d^{\rm fid}}{H r_d}$$
Measures distortion of BAO scale along line-of-sight.
What is in the formula
alpha_parallelvariableBAO scale distortion parameter along line-of-sight — dimensionless parameter
H_fidvariablefiducial Hubble parameter — hubble parameter metre per second per metre
r_d_fidvariablefiducial sound horizon at drag epoch — length metre
Hvariabletrue Hubble parameter — hubble parameter metre per second per metre
r_dvariabletrue sound horizon at drag epoch — length metre
α_\parallel(z)=\frac{h^{\rmfid}(z)r_d^{\rmfid}}{h^{\rmmodel}(z)r_d^{\rmmodel}} · 2607.18376v1
$$\omega = \sqrt{k/m}, \quad A = \sqrt{2E/k}$$
Frequency and amplitude of a harmonic oscillator depend on mass and stiffness.
What is in the formula
ωvariableangular frequency — angular frequency radian per second
kvariablespring constant — spring constant newton per metre
mvariablemass — mass kilogram
Avariableamplitude — amplitude metre
Evariabletotal energy — energy joule
√operatorsquare root operation — square root
ω=\sqrt{k/m},\quada=\sqrt{2e/k} · 2606.23490

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