EVOLUTION OF THE PRIMORDIAL MAGNETIC FIELD I. INITIAL MORPHOLOGY AND STRENGTH

The morphology and strength of the primordial magnetic field which is generated spontaneously in the early universe are studied for three models: (1) inflation (2) primordial magnetized bubble and (3) primordial turbulence models, We calculate the power spectra of magnetic field that are scale-free and proportional to $k^{1.5},k^{3{\sim}4}$ and $k^{2/3}$, respectively. The configurations of magnetic field having these power spectra are visualized. To constrain the present strength of the primordial magnetic field we calculate the anisotropy of the microwave background radiation in Bianchi type I universe with globally homogeneous magnetic field. From the COBE limit of the quadrupole moment of $({\delta}T/T)_{l=2}$ the present strength of horizen-scale magnetic fields $B_p$ is constrained to be less than $9{\times}10^{-8}G$.