Primordial Magnetic Field Amplification from Turbulent Reheating

TL;DR

This paper investigates how primordial magnetic fields could be amplified during the reheating phase of the early universe through a stochastic dynamo mechanism driven by turbulence, suggesting a more complex evolution than simple flux freezing.

Contribution

It introduces a model of magnetic field amplification during reheating using a stochastic dynamo approach with a charged scalar field, highlighting the role of turbulence and kinetic helicity.

Findings

Reynolds number $Re(k)$ computed for the reheating phase.

Characteristic turbulence decay time $t_{d}$ and pair annihilation time $t_{a}$ determined, with $t_{a}<< t_{d}$.

Estimated weak amplification factor of seed magnetic fields due to stochastic dynamo.

Abstract

We analyze the possibility of primordial magnetic field amplification by a stochastic large scale kinematic dynamo during reheating. We consider a charged scalar field minimally coupled to gravity. During inflation this field is assumed to be in its vacuum state. At the transition to reheating the state of the field changes to a many particle/anti-particle state. We characterize that state as a fluid flow of zero mean velocity but with a stochastic velocity field. We compute the scale-dependent Reynolds number $% Re(k)$, and the characteristic times for decay of turbulence, $t_{d}$ and pair annihilation $t_{a}$, finding $t_{a}<< t_{d}$. We calculate the rms value of the kinetic helicity of the flow over a scale $\mathcal{L}$ and show that it does not vanish. We use this result to estimate the amplification factor of a seed field from the stochastic kinematic dynamo equations. Although this effect is weak, it shows that the evolution of the cosmic magnetic field from reheating to galaxy formation may well be more complex than as dictated by simple flux freezing.