Tight-coupling approximation

The tight-coupling approximation expands the photon-baryon Boltzmann equations in powers of $k/\Gamma$ and $\mathcal{H}/\Gamma$, where $\Gamma$ is the Thomson scattering rate.

For baryon-loading ratio $R=3{\rho }_b/(4{\rho }_{\gamma })$, the photon-baryon sound speed is $c_s^2=1/[3(1+R)]$.