After the transition, neutrino-density perturbations evolve in a similar way to CDM on scales larger than a free-streaming length, and are damped on smaller scales. The comoving free-streaming length is defined analogously to a Jeans length, by replacing the sound of speed by $v_\mathrm{th}$, i.e., $\lambda_\mathrm{fs}(t)=2\pi\sqrt{2/3}\,v_\mathrm{th}(t)/[a(t)H(t)]$. It decreases from the time of transition onwards as, $$\label{eq:kfs}
\lambda_\mathrm{fs} = 2 \pi \times 1.2 (1+z)^{1/2} (m_\nu/1\,\mathrm{eV})^{-1}({\Omega_{\mathrm{m}}}h^2)^{-1/2} \,\,\mathrm{Mpc},$$ which is valid at high redshift. The maximum occurs at the transition and is given by, $$\label{eq:kfsmax}
\lambda^*_\mathrm{fs}= 2\pi \times 55 ({\Omega_{\mathrm{m}}}h^2)^{-1/2}\left( \frac{m_\nu}{1\,\mathrm{eV}}\right)^{-1/2}h^{-1} \mathrm{Mpc}.$$ The density perturbations of the other components, in particular CDM, are affected by the presence of massive neutrinos as a consequence of the change in the background evolution, the change in the time of equality, and feedback from the neutrino perturbations. Roughly speaking, the effect of $m_\nu=1\mathrm{eV}$ neutrinos in the power spectrum is similar to the CDM effect on large scales $k=2\pi/\lambda < k_\mathrm{fs}(z_\mathrm{tr}) \simeq 0.01\,
\mathrm{Mpc}^{-1}$; a scale-dependent suppression of the power spectrum amplitude at intermediate scales $0.01\,\mathrm{Mpc}^{-1}\lesssim k < k_\mathrm{fs}(z=0)\simeq 0.5\,\mathrm{Mpc}^{-1}$; and a scale-independent suppression of amplitude at small scales $k \gtrsim 0.5\,\mathrm{Mpc}^{-1}$.

Various combinations of cosmological data have been used to constrain the neutrino mass. Using CMB data 