  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 $\frac{{\delta}B}{B}\sim{|{\Theta}|t}$.
