Evolution of Primordial Magnetic Fields from Phase Transitions

Abstract

We consider the evolution of primordial magnetic fields generated during cosmological, electroweak or QCD, phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover "universal" laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low viscosity) regime. In particular, we show that during the radiation dominated epoch, energy and correlation length of non-helical magnetic fields scale as conformal time to the powers -1/2 and +1/2, respectively. For helical magnetic fields, energy and correlation length scale as conformal time to the powers -1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of magnetic field generated during the QCD phase transition could reach $\sim 10^{-9}$\,G with the present day correlation length $\sim 50$ kpc. The fields generated at the electroweak phase transition could be as strong as $\sim 10^{-10}$ G with correlation lengths reaching $\sim 0.3$\,kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields.

10 pages, 7 figures, minor changes, accepted for publication in PRD

References in corpus (12)

• On the Origin of Cosmic Magnetic Fields
• Lower limit on the strength and filling factor of extragalactic magnetic fields
• Magnetic field production during preheating at the electroweak scale
• Magnetic Fields from QCD Phase Transitions
• Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence
• Primordial magnetic field limits from cosmological data
• Helical Magnetic Fields from Sphaleron Decay and Baryogenesis
• Numerical simulations of the decay of primordial magnetic turbulence
• The Evolution of the Large-Scale Tail of Primordial Magnetic Fields
• Galactic and Extragalactic Magnetic Fields
• Time Evolution of the Large-Scale Tail of Nonhelical Primordial Magnetic Fields with Back-Reaction of the Turbulent Medium
• Role of Charged Gauge Fields in Generating Magnetic Seed Fields in Bubble Collisions during the Cosmological Electroweak Phase Transition

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• Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field
• Baryon Asymmetry and Gravitational Waves from Pseudoscalar Inflation
• The turbulent chiral-magnetic cascade in the early universe
• Magnetic Helicity and Large Scale Magnetic Fields: A Primer
• Implications of a Primordial Magnetic Field for Magnetic Monopoles, Axions, and Dirac Neutrinos
• Cosmic Magnetism in Centimeter and Meter Wavelength Radio Astronomy
• Probing Intergalactic Magnetic Fields with Simulations of Electromagnetic Cascades
• Nonhelical turbulence and the inverse transfer of energy: A parameter study
• Two-scale analysis of solar magnetic helicity
• Generation of large-scale magnetic fields, non-Gaussianity, and primordial gravitational waves in inflationary cosmology
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• Fundamental Implications of Intergalactic Magnetic Field Observations
• On the Inverse Transfer of (Non-)Helical Magnetic Energy in a Decaying Magnetohydrodynamic Turbulence
• Primordial Magnetic Helicity from Stochastic Electric Currents
• Particle temperature and the Chiral Vortical Effect in the early universe
• Cross-helically forced and decaying hydromagnetic turbulence