Abstract
We study high-redshift structure formation and reionization in a ΛCDM 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 combined analysis of the recent Wilkinson Microwave Anisotropy Probe (WMAP) data and two other large-scale structure observations. We carry out high-resolution cosmological simulations and use them to study the formation of primordial gas clouds where the first stars are likely to form. While early structure forms hierarchically in the RSI model, quite similar to the standard power-law ΛCDM model, the reduced power on small scales causes a considerable delay in the formation epoch of low-mass (~106 M☉) "minihalos" compared with the ΛCDM model. The abundance of primordial star-forming gas clouds in such halos also differs by more than an order of magnitude at z > 15 between the two models. 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 ΛCDM model. By carrying out radiative transfer calculations, we also study reionization by stellar populations formed in galaxies. We show that, in order to reionize the universe by z ~ 7, the escape fraction of ultraviolet photons from galaxies in the RSI model must be as high as 0.6 throughout the redshift range 5 < z < 18 for a stellar population similar to that of the local universe. Even with a top-heavy initial 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 τe ~ 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.
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