Constraints on neutrino density and velocity isocurvature modes from
  WMAP-9 data
  We use WMAP 9-year and other CMB data to constrain cosmological models where
the primordial perturbations have both an adiabatic and a (possibly correlated)
neutrino density (NDI), neutrino velocity (NVI), or cold dark matter density
(CDI) isocurvature component. For NDI and CDI we use both a phenomenological
approach, where primordial perturbations are parametrized in terms of
amplitudes at two scales, and a slow-roll two-field inflation approach, where
slow-roll parameters are used as primary parameters. For NVI we use only the
phenomenological approach, since it is difficult to imagine a connection with
inflation. We find that in the NDI and NVI cases larger isocurvature fractions
are allowed than in the corresponding models with CDI. For uncorrelated
perturbations, the upper limit to the primordial NDI (NVI) fraction is 24%
(20%) at k = 0.002 Mpc^{-1} and 28% (16%) at k = 0.01 Mpc^{-1}. For maximally
correlated (anticorrelated) perturbations, the upper limit to the NDI fraction
is 3.0% (0.9%). The nonadiabatic contribution to the CMB temperature variance
can be as large as 10% (-13%) for the NDI (NVI) modes. Bayesian model
comparison favors pure adiabatic initial mode over the mixed primordial
adiabatic and NDI, NVI, or CDI perturbations. At best, the betting odds for a
mixed model (uncorrelated NDI) are 1:3.4 compared to the pure adiabatic model.
For the phenomenological generally correlated mixed models the odds are about
1:100, whereas the slow-roll approach leads to 1:13 (NDI) and 1:51 (CDI).
