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 nonzero 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 nonadiabaticity 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 1 sigma level: gamma <= 5.3 x 10(-3) (1.2 x 10(-2)) and Delta N-eff <= 0.16(0.40). CMBPol will further improve these constraints to gamma <= 1.5 x 10(-3) and Delta N-eff <= 0.043. Finally, we recast these bounds in terms of the background neutrino degeneracy parameter (xi) over bar and the corresponding perturbation amplitude sigma(xi), and compare with the bounds on (xi) over bar that can be derived from big bang nucleosynthesis (BBN).