Jeans length (${\lambda }_J=c_s\sqrt{\pi /(G\rho )}$)

With physical wavelength $2\pi /k$, the Jeans length is $2\pi /k_J$, where the Jeans wavenumber is $\sqrt{4\pi G\rho }/c_s$. Linear pressure support dominates gravity below this length, whereas longer wavelengths can grow. In an expanding background the growth also depends on the Hubble damping term, so the static threshold does not by itself give the time dependence.