The Epoch of Reionization in Models with Reduced Small Scale Power

Reducing the power on small scales relative to the `standard' LCDM model alleviates a number of possible discrepancies with observations, and is favored by the recent analysis of WMAP plus galaxy and Lyman-alpha forest data. Here, we investigate the epoch of reionization in several models normalized to WMAP on large scales, and with sufficiently reduced power on small scales to solve the halo concentration and substructure problems. These include a tilted model, the WMAP running-index model, and a Warm Dark Matter model. We assume that the Universe was reionized by stellar sources comprised of a combination of supermassive (~200 M_sun) Pop III stars and Pop II stars with a `normal' IMF. We find that in all of these models, structure formation and hence reionization occurs late, certainly at redshifts below ten, and more probably at z < 6. This is inconsistent (at 2 sigma) with the determination of z_reion ~ 17 from the WMAP temperature-polarization data and is only marginally consistent with SDSS quasar observations. The tension between the galactic-scale observations, which favor low-power models, and the early reionization favored by WMAP can only be resolved if the efficiency of Pop III star formation is dramatically higher than any current estimate, or if there is an exotic population of ionizing sources such as mini-quasars. Otherwise, we may have to live with the standard LCDM power spectrum, and solve the small-scale problems in some other way.