Rothman and Matzner  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 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  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 .
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  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.
|Physical and Relativistic Numerical Cosmology
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