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The origin of the observed large scale magnetic fields in the Universe is amystery. The seed of these magnetic fields has been attributed to physicalprocess in the early universe. In this work we provide a mechanism for thegeneration of a primordial magnetic field in the early universe via the Weibelinstability in the quark gluon plasma. The Weibel instability occurs in theplasma if there is an anisotropy in the particle distribution function of theparticles. In early universe, the velocity anisotropy required for Weibelinstability to operate is generated in the quark gluon plasma by the collapseof closed $Z(3)$ domain walls that arise in the deconfined phase of the QCD(above $T\sim 200$ MeV). Such large domains can arise in the context of certainlow energy scale inflationary models. The closed domains undergo supersoniccollapse and the velocity anisotropy is generated in the shocks produced in thewake of the collapsing domain walls. This results in a two stream Weibelinstability in the ultra-relativistic quark gluon plasma. The instability inturn generates strong magnetic fields in the plasma. We find that the fieldstrengths generated can be comparable to the equipartition energy density atthe QCD scale which is of the order of $10^{18}$ G.

Primordial Magnetic Field Via Weibel Instability In The Quark Gluon Plasma Phase