BBN constraints on dark radiation isocurvature
  The existence of dark radiation that is completely decoupled from the
standard model in the early Universe leaves open the possibility of an
associated dark radiation isocurvature mode. We show that the presence of dark
radiation isocurvature leads to spatial variation in the primordial abundances
of helium and deuterium due to spatial variation in $N_{\rm eff}$ during Big
Bang nucleosynthesis. We use the result to constrain the existence of such an
isocurvature mode on scales down to $\sim 1$ Mpc scales. By measuring the
excess variance in the primordial helium to hydrogen and deuterium to hydrogen
ratio in different galaxies, we constrain the variance in average isocurvature
in a galaxy to be less than $0.13/\Delta \bar{N}_{\rm eff}$ at 95\% confidence.
Here $\Delta \bar{N}_{\rm eff}$ is the spatially averaged increase in $N_{\rm
eff}$ due to the additional dark radiation component.
