Dynamo action at recombination epoch of open Friedmann universe spatial sections

TL;DR

This paper explores how magnetic fields could have been amplified during the recombination epoch of an open Friedmann universe through dynamo mechanisms influenced by negative spatial curvature, providing bounds on cosmic magnetic field evolution.

Contribution

It generalizes the relativistic GR-MHD dynamo equation to include mean-field effects and analyzes magnetic field growth in a negatively curved cosmological setting.

Findings

Magnetic field growth rate at recombination is approximately 10^{-9} yr^{-1}.

Negative curvature enhances dynamo effects during the recombination epoch.

Bounds are placed on curvature effects to explain present-day magnetic field strengths.

Abstract

Chicone et al [Comm Math Phys (1997)] investigated existence of fast dynamos by analyzing the spectrum kinematic magnetic dynamo. In real non-degenerate branch of the spectrum, the kinematic dynamo operator lies on a compact Riemannian 2D space of constant negative curvature. Here, generalization of Marklund and Clarkson [MNRAS (2005)], general relativistic GR-MHD dynamo equation to include mean-field dynamos is obtained. In the absence of kinetic helicity, adiabatic constant $\gamma={1/2}$ and gravitational colapse of negative Riemann curvature of spatial sections enhance dynamo effect $\frac{{\delta}B}{B}=2.6\times 10^{-1}$. Critical time where linear dynamo effects breaks down de to curvature. At recombination time, COBE temperature anisotropies, implies that magnetic field growth rate is ${\lambda}{\approx{10}^{-9}yr^{-1}}$. This places a bound on curvature till the recombination magnetic field is amplified to present value of $B_{0}=10^{-9}G$, by dynamo action. At present epoch, negative curvature becomes constant and the Chicone et al result is shown to be valid in cosmology. Since negative curvature is non-constant, Hilbert theorem which forbiddes negative constant curvature surfaces embeddeding in $\textbf{R}^{3}$ is bypassed.