Cosmologies of Bianchi Type i with a Uniform Magnetic Field

An analysis is presented of the effects of a uniform, primordial magnetic field upon spatially homogene- ous cosmological models with the anisotropic, Euclidean metric ds2 = d12 - A2(t)dx2 - B2(t)dy2 - W2(t)dz2. The stress-energy tensor consists of perfect-fluid matter with the equation of state PM = 7PM (0 «= y «= 1) and a uniform magnetic field of energy density PB Analytical solutions are obtained for four subcases, and all remaining cases are studied by numerical integration. Axisymmetric solutions (A = B) always emerge from point or pancake singularities, while non-axisymmetric solutions (A != B) always emerge from initial cigar or barrel singularities. The solutions are used in a cursory examination of the effects of a primordial magnetic field upon (a) the temperature isotropy of the observed 30 K cosmic microwave radiation, (b) the time when expansion anisotropies become small, and (c) primordial element formation