Cosmologies of Bianchi Type i with a Uniform Magnetic Field
Abstract
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 stressenergy tensor consists of perfectfluid 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 nonaxisymmetric 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
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1969
 DOI:
 10.1086/149875
 Bibcode:
 1969ApJ...155..379J