Cosmic dynamo analogue and decay of magnetic fields in 3D Ricci flows

TL;DR

This paper explores how magnetic fields decay or grow in curved 3D spaces influenced by Ricci flows, revealing that the cosmological constant affects dynamo action and magnetic field evolution, with implications for cosmology and laboratory analogues.

Contribution

It derives a covariant magnetic self-induced equation in Ricci flows, linking magnetic field behavior to curvature effects and cosmological constants, extending previous work to 3D Ricci flow contexts.

Findings

De Sitter cosmological constant enhances dynamo action.

Anti-de Sitter case allows magnetic field decay.

Magnetic decay rate is approximately -10^{-35} s^{-2}.

Abstract

Magnetic curvature effects, investigated by Barrow and Tsagas (BT) [Phys Rev D \textbf{77},(2008)],as a mechanism for magnetic field decay in open Friedmann universes (${\Lambda}<0$), 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 (${\Lambda}\ge{0}$), 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 (${\Lambda}<0$) 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 ${\gamma}\approx{-{\Lambda}}\approx{-10^{-35}s^{-2}}$ from corresponding cosmological constant ${\Lambda}$, showing that, even in the dynamo case, magnetic field growth is slower than de Sitter inflation, which strongly supports to BT result.