We present a model that rotating primordial blackholes(PBHs) produced at the end of inflation generate the random, non-oriented primordial magnetic field. PBHs are copiously produced as the Universe completes the cosmic phase transition via bubble nucleation and tunneling processes in the extended inflation hypothesis. The PBHs produced acquire angular momentum through the mutual tidal gravitational interaction. For PBHs of mass less than 1013g, one can show that the evaporation (photon) luminosity of PBHs exceeds the Eddington limit. Thus throughout the lifetime of the rotating PBH, radiation flow from the central blackhole along the Kerr-geodesic exerts torque to ambient plasma. In the process similar to the Bierman's battery mechanism electron current reaching up to the horizon scale is induced. For PBHs of Grand Unified Theories extended inflation with the symmetry breaking temperature of TGUT ~1010 GeV, which evaporate near decoupling, we find that they generate random, non-oriented magnetic fields of ~10-11G on the last-scattering surface on (the present comoving) scales of ~O(10)Mpc.

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 k1.5,k3~4 and k2/3, 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 (δT/T)l=2 the present strength of horizen-scale magnetic fields Bp is constrained to be less than 9 × 10-8G.