Large-scale magnetic fields from hydromagnetic turbulence in the very early universe

Abstract

We investigate hydromagnetic turbulence of primordial magnetic fields using magnetohydrodynamics ͑MHD͒ in an expanding universe. We present the basic, covariant MHD equations, find solutions for MHD waves in the early universe, and investigate the equations numerically for random magnetic fields in two spatial dimensions. We find the formation of magnetic structures at larger and larger scales as time goes on. In three dimensions we use a cascade ͑shell͒ model that has been rather successful in the study of certain aspects of hydrodynamic turbulence. Using such a model we find that after ϳ10 9 times the initial time the scale of the magnetic field fluctuation ͑in the comoving frame͒ has increased by 4-5 orders of magnitude as a consequence of an inverse cascade effect ͑i.e., transfer of energy from smaller to larger scales͒. Thus at large scales primordial magnetic fields are considerably stronger than expected from considerations which do not take into account the effects of MHD turbulence. ͓S0556-2821͑96͒02712-9͔ PACS number͑s͒: 95.30.Qd, 04.40.Nr, 98.62.En

Decay of magnetohydrodynamic turbulence from power-law initial conditions

“…A slope of −1.057 ± 0.004 is observed for q = 1 between τ = 8.7 × 10 −3 and τ = 8.7 × 10 −2 in reasonable agreement with Eq. (11). In FIG.…”

“…They exhibit an energy cascade in the presence of viscosities. We confine our study to a shell model proposed in [11,12] that enforces all the ideal 3DMHD invariants in the inviscid, unforced case, that reduces to the well-known GOY [14] model for fluid turbulence when magnetic terms are suppressed, has no adjustable parameters apart from the fluid and magnetic Reynolds numbers, and exhibits the same multiscaling (within error bars) as the 3DMHD equations.…”

“…Such initial conditions are of interest in the astrophysical context of the decay of power-law 'primordial' energy spectra [8]. We also derive bounds for the decay of the cross-and magnetic helicity.We then show by systematic numerical studies of a shell model for MHD turbulence [11,12] and an 80 3 pseudospectral DNS of the 3DMHD equations that, given power-law initial conditions, the kinetic and magnetic energies and the Taylor and integral scales follow the decay expressions mentioned above within a regime governed by the temporal evolution of the integral scales.…”

Multiscaling Anderson localization of cosmic electromagnetic fields

“…Large-scale electromagnetic fields are expected to be generated by the cosmological phase transitions (electroweak and QCD) [1]- [12] before the recombination time. On the other hand, before the recombination time the cosmic plasma is strongly fluctuating at the large scales due to the gravitational density perturbation.…”

Evolution of primordial magnetic fields

“…al. [26], who describe the plasma with relativistic magnetohydrodynamic equations and turbulent behaviour. However, they are unable to solve their equations analytically, and, instead, they attempt a numerical analysis in 2+1 dimensions.…”