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It is shown that the existence of the cosmic kinematic fast dynamos inBianchi type IX rotating cosmological models, faces severe difficulties, due tothe fact that in these models rotation increases without bounds, which isstrictly forbidden by CMB astronomical date which imposes strong bounds on itsrotation with respect with its rapid expansion. The only way out of thisdifficulty is to assume that at least one of the expansion directions of thisanisotropic universe decays as fast as the amplification rate of primordialmagnetic fields. A solution is found where only one direction of theanisotropic universe expands while the other two remain constants. We computean amplification of the seed magnetic field in the case where Bianchi IXdegenerates into de Sitter metric, fields amplify from 10^{-6}G to 10^{-5}G inspiral galaxies for a cosmological constant of the order$|{\Lambda}|<10^{33}s^{-2}$ and considering that the age of universe of theorder of 10^{10}yrs. Another example is given by the ABC chaotic flows in thepseudo-Riemannian spacetime representing the Kasner anisotropic nonsingularuniverse.

Chaotic flows and cosmic dynamos in anisotropic pseudo-Riemannian four-dimensional spacetime