One of the most debated issues in the theoretical modeling of cosmic reionization is the impact of small-mass gravitationally-bound structures. We carry out the first numerical investigation of the role of such sterile `minihaloes, which serve as self-shielding screens of ionizing photons. Minihaloes are too small to be properly resolved in current large-scale cosmological simulations, and thus we estimate their effects using a sub-grid model, considering two cases that bracket their effect within this framework. In the `extreme suppression case in which minihalo formation ceases once a region is partially ionized, their effect on cosmic reionization is modest, reducing the volume-averaged ionization fraction by an overall factor of less than 15%. In the other extreme, in which minihalo formation is never suppressed, they delay complete reionization as much as Delta z~2, in rough agreement with the results from a previous semi-analytical study by the authors. Thus, depending on the details of the minihalo formation process, their effect on the overall progress of reionization can range from modest to significant, but the minihalo photon consumption is by itself insufficient to force an extended reionization epoch.
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