Statistics of baryon isocurvature perturbations in the inflationary universe

The statistical distribution of baryon-number fluctuations, which may provide a proper initial condition for the minimal isocurvature scenario, is carefully investigated both analytically and numerically. For fluctuations associated with power-law inflation, we find that the distribution is highly non-Gaussian on scales of pregalactic star formation while it is Gaussian on scales of large-scale structure. On the other hand, in the pure de Sitter universe, it is shown to be Gaussian on any astrophysical scale. It is also discussed why the Gaussian nature appears in these models.