Cosmological constraints on the neutrino mass including systematic
  uncertainties
  When combining cosmological and oscillations results to constrain the
neutrino sector, the question of the propagation of systematic uncertainties is
often raised. We address this issue in the context of the derivation of an
upper bound on the sum of the neutrino masses ($\Sigma m_\nu$) with recent
cosmological data. This work is performed within the
${{\mathrm{\Lambda{CDM}}}}$ model extended to $\Sigma m_\nu$, for which we
advocate the use of three mass-degenerate neutrinos. We focus on the study of
systematic uncertainties linked to the foregrounds modelling in CMB data
analysis, and on the impact of the present knowledge of the reionisation
optical depth. This is done through the use of different likelihoods built from
Planck data. Limits on $\Sigma m_\nu$ are derived with various combinations of
data, including the latest Baryon Acoustic Oscillations (BAO) and Type Ia
Supernovae (SN) results. We also discuss the impact of the preference for
current CMB data for amplitudes of the gravitational lensing distortions higher
than expected within the ${{\mathrm{\Lambda{CDM}}}}$ model, and add the Planck
CMB lensing. We then derive a robust upper limit: $\Sigma m_\nu< 0.17\hbox{ eV
at }95\% \hbox{CL}$, including 0.01 eV of foreground systematics. We also
discuss the neutrino mass repartition and show that today's data do not allow
one to disentangle normal from inverted hierarchy. The impact on the other
cosmological parameters is also reported, for different assumptions on the
neutrino mass repartition, and different high and low multipole CMB
likelihoods.
