Primordial magnetic fields constrained by CMB anisotropies and dynamo
  cosmology
  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.
