The synthesis of light elements in turbulent cosmologies

Primordial nucleosynthesis is investigated in the vortex cosmologies conceived by Ozernoi and co-workers. The early evolution of non-relativistic and relativistic velocity fields within homogeneous and inhomogeneous anisotropic eddies is investigated in detail together with the occurrence of thermal equilibrium. The various conditions under which element synthesis can occur are delineated and the resulting abundances related to the maximum turbulent mass scale at recombination associated with protogalaxies. All dynamical effects depend essentially only upon the baryon density parameter, Ω, and w, the adiabatic fluid velocity at t_eq. The helium and deuterium abundances synthesized on different mass scales are determined and it is found that helium and deuterium abundances within the range of observation can only be obtained on galactic scales if $$\Omega\,\lt\,1.4\,\times\,{10}^{-2}$$. The effects of small-scale processes like clumping dissipation and shocks are also discussed. In conjunction with considerations of the microwave isotropy the results imply that if light elements are to be synthesized primordially then the turbulent cosmologies conflict with observation.