WMAP, neutrino degeneracy, and non-Gaussianity constraints on isocurvature perturbations in the curvaton model of inflation

In the curvaton model of inflation, where a second scalar field, the “curvaton,” is responsible for the observed inhomogeneity, a nonzero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino, cold dark matter and baryon components. We find that the current data can only place upper limits on the level of isocurvature perturbations. These can be translated into upper limits on the neutrino degeneracy parameter. In the case that lepton number is created before curvaton decay, we find that the limit on the neutrino degeneracy parameter is comparable with that obtained from big-bang nucleosynthesis. For the case that lepton number is created by curvaton decay we find that the absolute value of the non-Gaussianity parameter, $|f_{\mathrm{nl}}|,$ must be less than 10 (95% confidence interval).