  We reconstruct the neutrino mass as a function of redshift, $z$, from current
cosmological data using both standard binned priors and linear spline priors
with variable knots. Using cosmic microwave background temperature,
polarization and lensing data, in combination with distance measurements from
baryonic acoustic oscillations and supernovae, we find that the neutrino mass
is consistent with $\sum m_\nu(z)=$ const. We obtain a larger bound on the
neutrino mass at low redshifts coinciding with the onset of dark energy
domination, $\sum m_\nu(z=0)<1.41$ eV (95% CL). This result can be explained
either by the well-known degeneracy between $\sum m_\nu$ and $\Omega_\Lambda$
at low redshifts, or by models in which neutrino masses are generated very late
in the Universe. We convert our results into cosmological limits for models
with post-recombination neutrino decay and find $\sum m_\nu <0.19$ eV (95% CL),
which is below the sensitivity of the KATRIN experiment. Thus, a neutrino mass
discovery by KATRIN would hint towards models predicting both
post-recombination neutrino mass generation and subsequent relic neutrino
annihilation.
