Future constraints on neutrino isocurvature perturbations in the
  curvaton scenario
  In the curvaton scenario, residual isocurvature perturbations can be
imprinted in the cosmic neutrino component after the decay of the curvaton
field, implying in turn a non-zero chemical potential in the neutrino
distribution. We study the constraints that future experiments like Planck,
SPIDER or CMBPol will be able to put on the amplitude of isocurvature
perturbations in the neutrino component. We express our results in terms of the
square root \gamma of the non-adiabaticity parameter \alpha and of the extra
relativistic degrees of freedom \Delta N_eff. Assuming a fiducial model with
purely adiabatic fluctuations, we find that Planck (SPIDER) will be able to put
the following upper limits at the 1sigma level: \gamma < 5.3x10^-3 (1.2x10^-2)
and \Delta N_eff < 0.16 (0.40) . CMBPol will further improve these constraints
to \gamma < 1.5x10^-3 and \Delta N_eff < 0.043. Finally, we recast these bounds
in terms of the background neutrino degeneracy parameter \xi\ and the
corresponding perturbation amplitude \sigma_\xi, and compare with the bounds on
\xi\ that can be derived from Big Bang Nucleosynthesis.
