Distribution function of nuclei from $e^{\pm }$ scattering in the presence of a strong primordial magnetic field

Abstract

The amplitude of the primordial magnetic field (PMF) is constrained from observational limits on primordial nuclear abundances. Within this constraint, it is possible that nuclear motion is regulated by Coulomb scattering with electrons and positrons ($e^{\pm }$'s), while $e^{\pm }$'s are affected by a PMF rather than collisions. For example, at a temperature of $10^9$ K, thermal nuclei typically experience $\sim 10^{21}$ scatterings per second that are dominated by very small angle scattering leading to minuscule changes in the nuclear kinetic energy of order $\mathcal{O}$(1) eV. In this paper the upper limit on the effects of a possible discretization of the $e^{\pm }$ momenta by the PMF on the nuclear momentum distribution is estimated under the extreme assumptions that the momentum of the $e^{\pm }$ is relaxed before and after Coulomb scattering to Landau levels, and that during Coulomb scattering the PMF is neglected. This assumption explicitly breaks the time reversal invariance of Coulomb scattering, and the Maxwell-Boltzmann distribution is not a trivial steady state solution of the Boltzmann equation under these assumptions. We numerically evaluate the collision terms in the Boltzmann equation, and show that the introduction of a special direction in the $e^{\pm }$ distribution by the PMF generates no directional dependence of the collisional destruction term of nuclei. Large anisotropies in the nuclear distribution function are then constrained from big bang nucleosynthesis. Ultimately, we conclude that a PMF does not significantly affect the isotropy or BBN.

arXiv comment8 pages, 3 figures, accepted for publication in PRD, divided into sections and minor changes added

References in corpus (37)

• The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present
• An Improved Distance to NGC 4258 and its Implications for the Hubble Constant
• Relieving the Hubble tension with primordial magnetic fields
• The First Magnetic Fields
• Progress on Cosmological Magnetic Fields
• Constraints on the Strength of Primordial Magnetic Fields from Big Bang Nucleosynthesis Revisited
• Non-extensive Statistics Solution to the Cosmological Lithium Problem
• Big Bang Nucleosynthesis Constraints on Primordial Magnetic Fields
• Constraints on Primordial Magnetic Fields from Planck combined with the South Pole Telescope CMB B-mode polarization measurements
• BICEP2 / Keck Array IX: New Bounds on Anisotropies of CMB Polarization Rotation and Implications for Axion-Like Particles and Primordial Magnetic Fields
• Updated constraint on a primordial magnetic field during big bang nucleosynthesis and a formulation of field effects
• Generation of Cosmic Magnetic Fields and Gravitational Waves at Neutrino Decoupling
• Constraints on primordial magnetic fields from magnetically-induced perturbations: current status and future perspectives with LiteBIRD and future ground based experiments
• Improved CMB anisotropy constraints on primordial magnetic fields from the post-recombination ionization history
• Big Bang Nucleosynthesis with an Inhomogeneous Primordial Magnetic Field Strength
• Insight into primordial magnetic fields from 21-cm line observation with EDGES experiment
• Constraining the primordial magnetic field with dwarf galaxy simulations
• Current and Future Constraints on Primordial Magnetic Fields
• Simulations and observational tests of primordial magnetic fields from Cosmic Microwave Background constraints
• Big Bang nucleosynthesis with a non-Maxwellian distribution
• The primordial magnetic field in our cosmic backyard
• Limits on primordial magnetic fields from direct detection experiments of gravitational wave background
• Searching for Primordial Magnetic Fields with CMB B-modes
• Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation
• Constraint on Primordial Magnetic Fields In the Light of ARCADE 2 and EDGES Observations
• Magnetic helicity evolution in a periodic domain with imposed field
• Chemical separation of primordial Li${}^{+}$ during structure formation caused by nanogauss magnetic field
• Analysis of the Multi-component Relativistic Boltzmann Equation for Electron Scattering in Big Bang Nucleosynthesis
• On the relative velocity distribution for general statistics and an application to big-bang nucleosynthesis under Tsallis statistics
• Relativistic Electron Scattering and Big Bang Nucleosynthesis
• Primordial magnetic fields during the cosmic dawn in light of EDGES 21-cm signal
• Screening corrections to Electron Capture Rates and resulting constraints on Primordial Magnetic Fields
• An upper limit on primordial magnetic fields from ultra-faint dwarf galaxies
• Small-scale CMB anisotropies induced by the primordial magnetic fields
• Initial Li Abundances in the Protogalaxy and Globular Clusters Based upon the Chemical Separation and Hierarchical Structure Formation
• Impact of a primordial magnetic field on cosmic microwave background $B$ modes with weak lensing
• Dark Matter Freeze Out with Tsallis Statistics in the Early Universe

Cited by in corpus (2)

• Big Bang Nucleosynthesis Limits and Relic Gravitational Waves Detection Prospects
• Imprints of primordial magnetic fields on intrinsic alignments of galaxies