Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology

TL;DR

This paper investigates primordial magnetic fields using cosmic dynamo theory, Riemannian curvature effects, and CMB anisotropies, providing new estimates for magnetic field growth rates and strengths in the early universe.

Contribution

It applies cosmic dynamo models with Riemannian curvature considerations to constrain primordial magnetic fields based on CMB data, offering novel estimates of magnetic field growth and magnitude.

Findings

Primordial magnetic field estimated at ~10^{-6} G at 1 second after Big Bang.

Computed magnetic growth rate consistent with COBE data and dynamo theory.

Demonstrated the influence of cosmic curvature on magnetic field amplification.

Abstract

Magneto-curvature stresses could deform magnetic field lines and this would give rise to back reaction and restoring magnetic stresses [Tsagas, PRL (2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the expansion to be slow down in spatial section of negative Riemann curvatures. From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D manifold implies negatively constant Riemannian curvature, here one applies the Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In absence of advection a fast dynamo is also obtained. Viscous and restoring forces on stretching particles decrease, as magnetic rates increase. From COBE data ($\frac{{\delta}B}{B}\approx{10^{-5}}$), one computes stretching $\frac{{\delta}V^{y}}{V^{y}}=1.5\frac{{\delta}B}{B}\approx{1.5{\times}10^{-5}}$. Zeldovich et al has computed the maximum magnetic growth rate as ${\gamma}_{max}\approx{8.0{\times}10^{-1}t^{-1}}$. From COBE data one computes a lower growth rate for the magnetic field as ${\gamma}_{COBE}\approx{6.0{\times}10^{-6}t^{-1}}$, well-within Zeldovich et al estimate. Instead of the Harrison value $B\approx{t^{{4/3}}}$ one obtains the lower primordial field $B\approx{10^{-6}t}$ which yields the $B\approx{10^{-6}G}$ at the $1s$ Big Bang time.