Cosmic reionization constraints on the nature of cosmological perturbations

Abstract

We study the reionization history of the Universe in cosmological models with non-Gaussian density fluctuations, taking them to have a renormalized $χ^2$ probability distribution function parametrized by the number of degrees of freedom, $ν$. We compute the ionization history using a simple semi-analytical model, considering various possibilities for the astrophysics of reionization. In all our models we require that reionization is completed prior to $z=6$, as required by the measurement of the Gunn--Peterson optical depth from the spectra of high-redshift quasars. We confirm previous results demonstrating that such a non-Gaussian distribution leads to a slower reionization as compared to the Gaussian case. We further show that the recent WMAP three-year measurement of the optical depth due to electron scattering, $τ=0.09 \pm 0.03$, weakly constrains the allowed deviations from Gaussianity on the small scales relevant to reionization if a constant spectral index is assumed. We also confirm the need for a significant suppression of star formation in mini-halos, which increases dramatically as we decrease $ν$.