Rotation and helicity as dynamo generators in idealized plasma cosmologies

Recently Kleides et al [IJMPA \textbf{11}, 1697 (2008)] found a growing rate for magnetic fields in ideal plasma cosmologies by making use of general relativistic Friedmann model. This growth rate of $\frac{{\delta}B}{B}\sim{{(\frac{t}{t_{H}})}^{{1/4}}}$ indicates the presence of a slow dynamo in the universe. More recently Hasseein [Phys Plasmas (2009)] have also investigate Beltrami magnetic fields in plasma universe. Here general relativistic(GR) MHD dynamo equation, recently given by Clarkson and Marklund [Monthly Not Roy Astr Soc (2005)] is used to investigate the relation between collapsing of the isotropic universe and dynamo action in ideal and dissipative cosmologies. Dynamo action can be supported in these phases as long as the kinetic helicity overcomes universe diffusion effects. A cosmological Beltrami flow in 3D shows that helicities may act constructively on gravitational collapse and enhance dynamo action. A slow dynamo action is found in the static Einstein universe also filled with a Beltrami flow. A rotating, shear-free Bianchi type-IX universe, is obtained, by magnetically perturbing the Einstein static model inducing slow dynamos in the model. Magnetic field growth of $B\approx{t}$, which is stronger than Harrison estimate of $B\approx{t^{{4/5}}}$ is obtained. CMB limits on the expansion, global rotation and slow dynamos are given and a less slower dynamo than the one obtained by Kleides et al, is found with $\frac{{\delta}B}{B}\sim{|{\Theta}|t}$.