  The first-year Wilkinson Microwave Anisotropy Probe data suggest a high
optical depth for Thomson scattering of 0.17 +/- 0.04, implying that the
universe was reionized at an early epoch, z ~ 20. Such early reionization is
likely to be caused by UV photons from first stars, but it appears that the
observed high optical depth can be reconciled within the standard structure
formation model only if star-formation in the early universe was extremely
efficient. With normal star-formation efficiencies, cosmological models with
non-Gaussian density fluctuations may circumvent this conflict as high density
peaks collapse at an earlier epoch than in models with Gaussian fluctuations.
We study cosmic reionization in non-Gaussian models and explore to what extent,
within available constraints, non-Gaussianities affect the reionization
history. For mild non-Gaussian fluctuations at redshifts of 30 to 50, the
increase in optical depth remains at a level of a few percent and appears
unlikely to aid significantly in explaining the measured high optical depth. On
the other hand, within available observational constraints, increasing the
non-Gaussian nature of density fluctuations can easily reproduce the optical
depth and may remain viable in underlying models of non-Gaussianity with a
scale-dependence.
