  Cosmological parameter estimation exercises usually make the approximation
that the three standard neutrinos have degenerate mass, which is at odds with
recent terrestrial measurements of the difference in the square of neutrino
masses. In this paper we examine whether the use of this approximation is
justified for the cosmic microwave background (CMB) spectrum, matter power
spectrum and the CMB lensing potential power spectrum. We find that, assuming
m^2_{23} ~ 2.5x10^{-3}$eV^2 in agreement with recent Earth based measurements
of atmospheric neutrino oscillations, the correction due to non-degeneracy is
of the order of precision of present numerical codes and undetectable for the
foreseeable future for the CMB and matter power spectra. An ambitious
experiment that could reconstruct the lensing potential power spectrum to the
cosmic variance limit up to l~1000 will have to take the effect into account in
order to avoid biases. The degeneracies with other parameters, however, will
make the detection of the neutrino mass difference impossible. We also show
that relaxing the bound on the neutrino mass difference will also increase the
error-bar on the sum of neutrino masses by a factor of up to a few. For exotic
models with significantly non-degenerate neutrinos the corrections due to
non-degeneracy could become important for all the cosmological probes discussed
here.
