Early Structure Formation and Reionization in a Cosmological Model with a Running Primordial Power Spectrum

(abridged) We study high redshift structure formation and reionization in a LCDM universe under the assumption that the spectral power index of primordial density fluctuations is a function of length scale. We adopt a particular formulation of the running spectral index (RSI) model as suggested by the recent WMAP data. While early structure forms hierarchically in the RSI model, the reduced power on small scales causes a considerable delay in the formation epoch of low mass (~ 10^6 Msun) ``mini-halos'' compared to the LCDM model. The extremely small number of gas clouds in the RSI model indicates that reionization is initiated later than z<15, generally resulting in a smaller total Thomson optical depth than in the LCDM model. By carrying out radiative transfer calculations, we also study reionization by stellar populations formed in galaxies. Even with a top-heavy intial mass function representing an early population of massive stars and/or an extraordinarily high photon emission rate from galaxies, the total optical depth can only be as large as tau ~ 0.1 for reasonable models of early star-formation. The RSI model is thus in conflict with the large Thomson optical depth inferred by the WMAP satellite.