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 ν-ν→ee⁺ dissipation is shown to lower both X(⁴He) and X(D) from the standard value for certain values of the initial shear. More sophisticated models are developed which include a new anisotropy formalism, νν→νν scatterings, and the effect of neutrino blue-shifts on the weak reaction rates. In the most realistic model, X(⁴He) 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(⁴He) ̃ \~<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_ν~30 eV. If all neutrinos are massless we find a limit approximately a factor of ten weaker than the observational quadrupole temperature-anisotropy limit.