Chaotic fast dynamo in Bianchi type - IX cosmological model July 25 , 2009

Magnetic curvature effects in Einstein general relativistic (GR) open Friedmann universe , has been investigated by Barrow and Tsagas (BT) [Phys Rev D 77,(2008)]. They demonstrated that this mechanism induces a magnetic field decay. In this report, one shows that by using the GR-(3+1)-space-time magnetohydrodynamic (MHD) induction equation derived by Marklund and Clarkson (CM) [MNRAS (2004)], two examples of GR cosmological models displays distinct dynamo speeds. The first, which is the usual static Einstein universe filled with a Beltrami flow, presents a slow dynamo behaviour. The other, a Bianchi type-IX universe, considered in the comoving frame and non-hypersurface orthogonal coordinates, presents a fast dynamo behaviour when the universe undergoes a contracting phase, while the magnetic field decays when the universe is considered to be highly conductive. In Einstein universe, Vishik anti-fast dynamo theorem applies [Garcia de Andrade,Phys Plasmas 15]. Zero-effective eigenvalue of magnetic field growth rate induces a fast dynamo in Bianchi type-IX model.