In the curvaton model of inflation , where a second scalar field , the ‘ curvaton ’ , is responsible for the observed inhomogeneity , a non-zero neutrino degeneracy may lead to a characteristic pattern of isocurvature perturbations in the neutrino , cold dark matter and baryon components .
We find 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 _ { nl } | , must be less than 10 ( 95 % confidence interval ) .