Cosmic Variance In the Transparency of the Intergalactic Medium After   Reionization
  Following the completion of cosmic reionization, the mean-free-path of ionizing photons was set by a population of Ly-limit absorbers. As the mean-free-path steadily grew, the intensity of the ionizing background also grew, thus lowering the residual neutral fraction of hydrogen in ionization equilibrium throughout the diffuse intergalactic medium (IGM). Ly-alpha photons provide a sensitive probe for tracing the distribution of this residual hydrogen at the end of reionization. Here we calculate the cosmic variance among different lines-of-sight in the distribution of the mean Ly-alpha optical depths. We find fractional variations in the effective post-reionization optical depth that are of order unity on a scale of ~100 co-moving Mpc, in agreement with observations towards high-redshift quasars. Significant contributions to these variations are provided by the cosmic variance in the density contrast on the scale of the mean-free-path for ionizing photons, and by fluctuations in the ionizing background induced by delayed or enhanced structure formation. Cosmic variance results in a highly asymmetric distribution of transmission through the IGM, with fractional fluctuations in Ly-alpha transmission that ar larger than in Ly-beta transmission. 
Stuart Wyithe & Abraham Loeb