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.