Rothman and Matzner [48] considered primordial nucleosynthesis in anisotropic cosmologies, solving the strong reaction equations leading to He. They find that the concentration of He increases with increasing shear; this is due to time scale effects and the competition between dissipation and enhanced reaction rates from photon heating and neutrino blue shifts. Their results have been used to place a limit on anisotropy at the epoch of nucleosynthesis. Kurki-Suonio and Matzner [38] extended this work to include 30 strong 2-particle reactions involving nuclei with mass numbers , and to demonstrate the effects of anisotropy on the cosmologically significant isotopes H, He, He and Li as a function of the baryon to photon ratio. They conclude that the effect of anisotropy on H and He is not significant, and the abundances of He and Li increase with anisotropy in accord with [48].

Furthermore, it is possible that neutron diffusion, the process whereby neutrons diffuse out from regions of very high baryon density just before nucleosynthesis, can affect the neutron to proton ratio in such a way as to enhance deuterium and reduce He compared to a homogeneous model. However, plane symmetric, general relativistic simulations with neutron diffusion [39] show that the neutrons diffuse back into the high density regions once nucleosynthesis begins there - thereby wiping out the effect. As a result, although inhomogeneities influence the element abundances, they do so at a much smaller degree then previously speculated. The numerical simulations also demonstrate that, because of the back diffusion, a cosmological model with a critical baryon density cannot be made consistent with helium and deuterium observations, even with substantial baryon inhomogeneities and the anticipated neutron diffusion effect.

Computational Cosmology: from the Early Universe to the
Large Scale Structure
Peter Anninos
http://www.livingreviews.org/lrr-1998-9
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