Isocurvature perturbations in extra radiation
  Recent cosmological observations, including measurements of the CMB anisotropy and the primordial helium abundance, indicate the existence of an extra radiation component in the Universe beyond the standard three neutrino species. In this paper we explore the possibility that the extra radiation has isocurvatrue fluctuations. A general formalism to evaluate isocurvature perturbations in the extra radiation is provided in the mixed inflaton-curvaton system, where the extra radiation is produced by the decay of both scalar fields. We also derive constraints on the abundance of the extra radiation and the amount of its isocurvature perturbation. Current observational data favors the existence of an extra radiation component, but does not indicate its having isocurvature perturbation. These constraints are applied to some particle physics motivated models. If future observations detect isocurvature perturbations in the extra radiation, it will give us a hint to the origin of the extra radiation. 
Masahiro Kawasaki, Koichi Miyamoto, Kazunori Nakayama, Toyokazu   Sekiguchi
astro-ph.CO hep-ph