Eur. Phys. J. Plus (2011) 126: 116
https://doi.org/10.1140/epjp/i2011-11116-7

Regular Article

Decay of magnetic fields in de Sitter and FRW universes

¹ Departamento de Física Teórica, IF, UERJ, Rua São Francisco Xavier 524, CEP:20550 Maracanã, Rio de Janeiro, RJ, Brazil
² Departamento de Matemáticas, Universidad de Murcia - Campus de Espinardo, 30100, Murcia, Spain

^* e-mail: garcia@dft.if.uerj.br

Received: 24 July 2011
Revised: 4 October 2011
Accepted: 10 October 2011
Published online: 30 November 2011

Abstract

Magnetic curvature effects, investigated by Barrow and Tsagas (Phys. Rev. D 77, 107302 (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-induction equation is obtained. The presence of these curvature effects indicates that de Sitter cosmological constant (Λ ≥ 0 leads to enhancement in the fast kinematic dynamo action which induces a stretching in plasma flows. From the magnetic growth rate, the strong shear case implies an anti-de Sitter case (Λ < 0) where BT magnetic decaying fields are possible. For weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in the (3 + 1)-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In the de Sitter analogue there is a decay rate of γ ≈ −Λ ≈ −10⁻³⁵ s⁻² from the corresponding cosmological constant Λ. This shows that, even in the dynamo case, the magnetic field growth is slower than de Sitter inflation, which renders strongly support to BT result.