Photon-baryon fluid

Before recombination, frequent Thomson scattering couples photons, electrons, and baryons into an acoustic fluid.

Table of contents
- Tight-coupling approximation Photon-baryon fluid
  - Photon-baryon sound speed Tight-coupling approximation
- Sound horizon Photon-baryon fluid

Tight-coupling approximation

The tight-coupling approximation expands the photon-baryon Boltzmann equations in powers of

k /Γ

and

H /Γ

, where

Γ

is the Thomson scattering rate.

Photon-baryon sound speed ( $c_{s}^{2}$ )

For baryon-loading ratio

R = 3 ρ_{b} / (4 ρ_{γ})

, the photon-baryon sound speed is

c_{s}^{2} = 1/ [3 (1 + R)]

.

Sound horizon ( $r_{s}$ )

The comoving sound horizon is the distance traveled by an acoustic wave,

r_{s} (η) = \int_{0}^{η} c_{s} (η^{'}) d η^{'} .

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