Nucleosynthesis in anisotropic cosmologies revisited

The subject of primordial nucleosynthesis in anisotropic cosmologies is reinvestigated. Simple time-scale models are examined and shown to be inadequate to describe the physics of anisotropic nucleosynthesis. A simple model including $\nu \bar{\nu }\to e{e}^{+}$ dissipation is shown to lower both $X\left({}_{}{}^4{}_{}{}^{}\mathrm{He}\right)$ and $X\left(\mathrm{D}\right)$ from the standard value for certain values of the initial shear. More sophisticated models are developed which include a new anisotropy formalism, $\nu \nu \to \nu \nu$ scatterings, and the effect of neutrino blue-shifts on the weak reaction rates. In the most realistic model, $X\left({}_{}{}^4{}_{}{}^{}\mathrm{He}\right)$ is found to increase sharply with increasing shear, but not primarily for the reasons given in time-scale arguments. New limits are placed on anisotropy at the epoch of nucleosynthesis. Limits on the quadrupole anisotropy at nucleosynthesis put limits on the microwave-temperature quadrupole anisotropy now. Estimates of the current microwave-temperature anisotropy, based on the requirement $X\left({}_{}{}^4{}_{}{}^{}\mathrm{He}\right)\widetilde{<}0.26$ (mass fraction) gives limits approximately a factor of 10 smaller (stronger) than current observational limits on the temperature anisotropy, if there is a massive neutrino, $m_{\nu }\sim 30$ eV. If all neutrinos are massless we find a limit approximately a factor of ten weaker than the observational quadrupole temperature-anisotropy limit.