= Baryon Jeans length across recombination
Before <cosmological recombination>, <photon-baryon sound speed> controls the baryonic <comoving Jeans length>. The tightly coupled <photon-baryon fluid> has $c_s^2=c^2/[3(1+R_b)]$, where $R_b=3\bar\rho_b/(4\bar\rho_\gamma)\propto a$. Using total background density in the instantaneous dynamical Jeans estimate, the scale grows as $a$ during <radiation domination>, approaches a plateau in strongly baryon-loaded <matter domination>, and drops when <photon decoupling> removes photon pressure support. Subsequently, adiabatic monatomic-gas cooling gives $T_b\propto a^{-2}$ and a <comoving Jeans length> proportional to $a^{-1/2}$. Residual <Compton scattering> can delay that cooling law.
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