Fluctuations in the Ionizing Background During and After Helium   Reionization
  The radiation background above the ionization edge of HeII varies strongly during and after helium reionization, because the attenuation length of such photons is relatively short (<40 Mpc) and because the ionizing sources (quasars) are rare. Here we construct analytic and Monte Carlo models to examine these fluctuations, including, for the first time, those during the reionization era itself. In agreement with detailed numerical simulations, our analytic model for the post-reionization Universe predicts order-of-magnitude fluctuations in the HeII ionization rate. Observations of the hardness ratio between HeII/HI show even larger fluctuations, which may be due to more complicated radiative transfer effects. During reionization, the fluctuations are even stronger. In contrast to hydrogen reionization, our model predicts that regions with strong HeII Lyman-alpha forest transmission should be reasonably common even during the beginning stages of reionization, because of strong illumination from bright quasars. Partly due to this, the mean ionizing background does not evolve strongly during and after helium reionization; it is roughly proportional to the filling fraction of HeIII regions. On the other hand, regions full of HeII and also "fossil" ionized regions that contain no (or few) active sources appear as strong IGM absorbers. Their presence exaggerates the evolution of the hardness ratio, making it evolve faster than naively expected during the reionization era. 
Steven Furlanetto (UCLA)