The epoch of reionization in models with reduced small-scale power

Reducing the power on small scales relative to the "standard'' Lambda cold dark matter (LambdaCDM) model alleviates a number of possible discrepancies with observations and is favored by the recent analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) plus galaxy and Lyalpha 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 composed of a combination of supermassive (similar to200 M.) Population III stars and Population II stars with a "normal'' initial mass function (IMF). We find that in all of these models, structure formation and hence reionization occurs late, certainly at redshifts below 10, and more probably at z less than or similar to 6. This is inconsistent (at 2 sigma) with the determination of z(reion) similar or equal to 17 from the WMAP temperature-polarization data and is only marginally consistent with Sloan Digital Sky Survey 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 Population III star formation is dramatically higher than any current estimate or if there is an exotic population of ionizing sources such as miniquasars. Otherwise, we may have to live with the standard LambdaCDM power spectrum and solve the small-scale problems in some other way.