Primordial Weibel instability

Abstract

We study the onset of vector instabilities in a post-inflationary epoch of the Universe as a mechanism for primordial magnetic fields amplification between the end of inflation and the electroweak (EW) transition. We assume the presence of a charged spectator scalar field arbitrarily coupled to gravity. This field is in its vacuum state during inflation, but becomes highly excited after the transition to the radiation dominance due to the gravitational particle creation. At the beginning of radiation era the ensuing state admits a hydrodynamic description. In particular since its high temperature, the fluid may be regarded as a conformal one. The large quantum fluctuations induced during reheating now become statistical fluctuations whereby an excess charge and anisotropic pressure will be observed in any finite domain. Under these conditions a Weibel instability could be triggered thus opposing the dilution of a primordial magnetic field because of the expansion of the Universe. The magnitude of the effect is determined by the size of the domain, the coupling to curvature of the field and the relaxation time of the fluid. We find that for scales of the order or smaller than the particle horizon at the EW phase transition, the Weibel instability can overcome the cosmic expansion provided that the reheating temperature of the Universe and the coupling of the scalar field to gravity are small enough.

Steady asymptotic equilibria in conformal relativistic fluids

“…It has been extended to include thermal [51] and turbulent [52] fluctuations. It has also been extended to charged plasmas to study the amplification of magnetic fields in the Early Universe [53]. By adding also the third moments, one obtains a theory which reproduces the propagators of the energy momentum tensor as derived from kinetic theory [39]; it also recovers the dynamics of the spin 2 degrees of freedom in the fluid as wave like, and not simply relaxational.…”