M ay 2 00 9 Cosmic dynamo analogue and decay of magnetic fields in 3 D Ricci flows May 13 , 2009

Magnetic curvature effects, investigated by Barrow and Tsagas (BT) [Phys Rev D 77,(2008)],as a mechanism for magnetic field decay in open Friedmann universes (Λ < 0), are applied to dynamo geometric Ricci flows in 3D curved substrate in laboratory. By simple derivation, a covariant three-dimensional magnetic self-induced equation, presence of these curvature effects, indicates that de Sitter cosmological constant (Λ ≥ 0), leads to enhancement in the fast kinematic dynamo action which adds to stretching of plasma flows. From the magnetic growth rate, the strong shear case, anti-de Sitter case (Λ < 0) BT magnetic decaying fields are possible while for weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in (3+1)-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In de Sitter analogue there is a decay rate of γ ≈ −Λ ≈ −10 −35 s −2 from corresponding cosmological constant Λ, showing that, even in the dynamo case, magnetic field growth is slower than de Sitter inflation, which strongly supports to BT result.