Effect of small-scale baryon inhomogeneity on cosmic nucleosynthesis

We consider the evolution of the nuclear abundances in a universe with inhomogeneities (induced by the quark-hadron phase transition) on a scale such that neutron diffusion is important before and during nucleosynthesis. We investigate a number of initial baryon density contrast ratios: R=10, 100, 1000; a number of high-density volume fractions: $f_V$=(1/4, (1/8, (1/16, and (1/64; and a number of geometries: planar, cylindrical with the higher density near the center, cylindrical with the higher density near the outer zone of computation (thin-walled tubes of higher density), spherical with the higher density near the center (isolated spherical regions of high density), and spherical with the higher density near the outer zones of the computation (a foam structure of high-density regions). We concentrate on three R=100 models. For a high-density [η=70×${10}^{\mathrm{-}10}$≡${\rho }_{\mathrm{baryon}}$(now) =4.3×${10}^{\mathrm{-}30}$ g ${\mathrm{cm}}^{\mathrm{-}3}$] universe that would be closed for Hubble parameter $H_0$=50 km/sec Mpc, we find disagreement in all three isotopes ${(}^2$H, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$) with observations, regardless of the scale $r_i$ of the inhomogeneity; for η=3×${10}^{\mathrm{-}10}$ and η=7×${10}^{\mathrm{-}10}$, ‘‘low’’- and ‘‘high’’-standard values (η=3×${10}^{\mathrm{-}10}$ corresponds in the homogeneous case to the absolute minimum of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ production), we find that for inhomogeneity distance scales typical of those expected at the quark-hadron transition, i.e., $r_i$≲100 m, then ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ abundances remain in agreement with observational values, and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ is also not much changed from its value in a homogeneous cosmology.