Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology

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.

Dept of theoretical physics-UERJ-Brasil

References in corpus (2)

• Two-dimensional one-component plasma on a Flamm's paraboloid
• Oscillating Ponomarenko dynamo in the highly conducting limit

Cited by in corpus (1)

• Current status of turbulent dynamo theory: From large-scale to small-scale dynamos