Primordial Weibel instability

We study the onset of vector instabilities in the post-inflationary epoch of the Universe as a mechanism for primordial magnetic fields amplification. We assume the pres-ence of a charged spectator scalar field arbitrarily coupled to gravity during Inflation in its vacuum de Sitter state. Gravitational particle creation takes place at the transition from In-flation to the subsequent Reheating stage and thus the vacuum field state becomes an excited many particles one. Consequently this state can be described as a real fluid, and we build out the hydrodynamic framework using second order theories for relativistic fluids with a relax-ation time prescription for the collision integral. Given the high-temp erature regime and the vanishing scalar curvature of the Universe during Reheating (radiation-dominated-type era), the fluid can be regarded as a conformal one. The large quantum fluctuations induced by the rapid transition from inflationary to effectively radiation dominated expansion become statistical fluctuations whereby both a charge excess and anisotropic pressures are produced in any finite domain. The precise magnitude of the effect for each scale is determined by the size of the averaging domain and the coupling to curvature. We look at domains which are larger than the horizon at the beginning of Reheating, but much smaller than our own horizon, and show that in a finite fraction of them the anisotropy and charge excess provide suitable conditions for a Weibel instability. If moreover the duration of reheating is shorter than the relaxation time of the fluid, then this instability can compensate or even overcome the conformal dilution of a primordial magnetic field. We show that the non-trivial topology of the magnetic field encoded in its magnetic helicity is also amplified if present.

Automated summary

In this study, we investigate the mechanism of amplification of primordial magnetic fields by studying the onset of vector instabilities in the post-inflationary epoch of the Universe. We consider the presence of a charged spectator scalar field during Inflation, and examine the effects of gravitational particle creation during the transition from Inflation to Reheating. We show that under certain conditions, the anisotropy and charge excess generated by the rapid transition can lead to a Weibel instability, which can compensate for the conformal dilution of the primordial magnetic field.