Stochastic isocurvature baryon fluctuations, baryon diffusion, and primordial nucleosynthesis

We examine effects on primordial nucleosynthesis from a truly random, one-dimensional spatial distribution in the baryon-to-photon ratio (eta). We generate stochastic fluctuation spectra characterized by different spectral indices and rms fluctuation amplitudes. For the first time we explicitly calculate the effects of baryon diffusion on the nucleosynthesis yields of such stochastic fluctuations. We also consider the collapse instability of large mass scale inhomogeneities. Our results are generally applicable to any primordial mechanism producing fluctuations in eta which can be characterized by a spectral index. In particular, these results apply to primordial isocurvature baryon fluctuation (PIB) models. The amplitudes of fluctuations that are scale-invariant in baryon density are found to be severely constrained by primordial nucleosynthesis. However, when the eta distribution is characterized by decreasing fluctuation amplitudes with increasing length scale, surprisingly large fluctuation amplitudes on the baryon diffusion scale are allowed.