= Jeans support versus forced baryon response
{title2=$\delta_B''+\mathcal H\delta_B'+c_s^2k^2\delta_B\simeq4\pi Ga^2\bar\rho_C\delta_C$}
When baryons are a small fraction of the gravitating matter, their perturbation is forced by the <cold dark matter> potential. Comparing pressure frequency $c_s^2k^2$ with $4\pi Ga^2\bar\rho_C$ yields the scale $\lambda_J=c_s\sqrt{\pi/(G\bar\rho_C)}$ for following the growing matter mode. It is not an absolute statement that every sub-Jeans baryon perturbation is zero or cannot be forced: a slowly varying response is $\delta_B\simeq(k_J^2/k^2)\delta_C$. In the pressureless limit the difference from CDM is a constant plus a decaying mode during <matter domination>, so baryons catch up in relative amplitude.
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