Constraints on a Primordial Magnetic Field

Abstract

We derive an upper limit of ${B}_{0}<3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}({\ensuremath{\Omega}}_{0}{h}_{50}^{2}{)}^{1/2}$ G on the present strength of any primordial homogeneous magnetic field. The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies. Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer (COBE) data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver. The limits we obtain on homogeneous magnetic fields are stronger than those imposed by nucleosynthesis.