Relativistic Chiral MHD with application to the early Universe
Abstract
We present a systematic derivation of the equations of relativistic chiral magnetohydrodynamics (MHD) for a plasma of charged fermions in an expanding universe. Through a combination of a coordinate transformation and a rescaling of the dynamical variables, we bring the full system to the same form as in the Minkowski metric, with the Hubble expansion surviving only in the chirality-flipping rate and the kinematic viscosity. Retaining all four contributions to both the electric and the axial current yields terms absent from standard chiral MHD: charge-density corrections to the evolution equations for the chemical potentials, and an electric current proportional to the charge chemical potential μ and the bulk velocity. The latter is mandated by current conservation, requires no chirality imbalance, and drives the charge-flow instability studied in a follow-up paper. For the radiation-dominated era, we evaluate all the coefficients in physical units and use them to estimate the magnetic Reynolds number, the attainable magnetic field strength, and the minimum temperature at which the chiral dynamo can operate. The resulting equations are cast in a form ready for direct numerical implementation.
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BibTeX
@misc{lark2026relativistic,
title = {{Relativistic Chiral MHD with application to the early Universe}},
author = {Deepen Lark and Jennifer Schober},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.22816},
eprint = {2607.22816},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22816},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relativistic Chiral MHD with application to the early Universe
AU - Deepen Lark
AU - Jennifer Schober
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2607.22816
UR - https://arxiv.org/abs/2607.22816
AB - We present a systematic derivation of the equations of relativistic chiral magnetohydrodynamics (MHD) for a plasma of charged fermions in an expanding universe. Through a combination of a coordinate transformation and a rescaling of the dynamical variables, we bring the full system to the same form as in the Minkowski metric, with the Hubble expansion surviving only in the chirality-flipping rate and the kinematic viscosity. Retaining all four contributions to both the electric and the axial current yields terms absent from standard chiral MHD: charge-density corrections to the evolution equations for the chemical potentials, and an electric current proportional to the charge chemical potential μ and the bulk velocity. The latter is mandated by current conservation, requires no chirality imbalance, and drives the charge-flow instability studied in a follow-up paper. For the radiation-dominated era, we evaluate all the coefficients in physical units and use them to estimate the magnetic Reynolds number, the attainable magnetic field strength, and the minimum temperature at which the chiral dynamo can operate. The resulting equations are cast in a form ready for direct numerical implementation.
ER -