Dynamo action at recombination epoch of open Friedmann universe spatial sections

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.