Primordial magnetic fields constrained from CMB anisotropies on dynamo cosmology

Abstract

Magneto-curvature stresses could deform magnetic field lines giving rise to back reaction and restoring magnetic stresses (Tsagas in Phys. Rev. Lett., 2001). Barrow and Tsagas (Phys. Rev. D, 2008) have shown that in Friedman universe the expansion slows down in its spatial section of negative Riemann curvature. Earlier, Chicone and Latushkin (Proc. Am. Math. Soc. 125(11):3391, 1995) proved that fast dynamos in compact 2D manifold implies negatively constant Riemannian curvature. Here one applies the Barrow-Tsagas ideas to cosmic dynamos of negative curvature. Fast dynamo, covariant stretching of Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection term on dynamo equations (Clarkson and Marklund in Mon. Not. R. Astron. Soc., 2005) is considered. In advection absence, slow dynamos are also obtained. It is shown the viscous and restoring forces on stretching particles decrease, as magnetic rates increase. From COBE data ($\frac{{\delta}B}{B}\approx{10^{-5}}$), one is able to compute the stretching $\frac{{\delta}V^{y}}{V^{y}}=1.5\frac{{\delta}B}{B}\approx{1.5{\times}10^{-5}}$. Zeldovich et al. have computed the maximum magnetic growth rate as γ _max ≈8.0×10⁻¹ t ⁻¹. From COBE data a lower growth rate as γ _COBE ≈6.0×10⁻⁶ t ⁻¹, is well-within Zeldovich et al estimate. Instead of Harrison value $B\approx{t^{\frac{4}{3}}}$ one obtains a lower primordial field B≈10⁻⁶ t which yields B≈10⁻⁶ G at 1 s Big Bang time.