Isochrones in primordial magnetic field evolution
Abstract
In the early universe, a primordial magnetic field undergoes a turbulent decay while its length scale increases due to an inverse cascade. The size of the largest processed eddy scales with the Alfvén speed and grows with time. In a diagram of Alfvén speed vs.\ length scale, all possible solutions must lie on a line through the origin with a slope proportional to the inverse of the present time. In principle, however, such lines can also be defined for earlier times. The lines for earlier times form isochrones that may be observationally accessible, for example through the magnetically driven stochastic gravitational wave background. However, the position and slope of these isochrones is sensitive to the zero point of the time. Here, we show that for any initial magnetic field, a proper time can be determined such that the resulting isochrones at early times are nearly parallel to those at late times, i.e., they have the same slope. We use two-dimensional numerical simulations of decaying MHD turbulence and vary the initial position of the peak of the magnetic energy spectrum. In this case, the evolution is governed by the conservation of anastrophy. A fit to the Alfvén time yields an accurate estimate of the factor by which the decay time is longer than the Alfvén time, while the offset in the fit provides an estimate of the proper time that needs to be added to the nominal time since the beginning of each simulation. We also find that the presence of an initial velocity field of realistic strength helps producing a more straight track from the beginning. The magnetic field parameters lie on universal isochrones even for early times. They provide a testable framework for magnetic fields generated at times as early as the end of inflation, starting with the time of reheating.
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BibTeX
@misc{brandenburg2026isochrones,
title = {{Isochrones in primordial magnetic field evolution}},
author = {Axel Brandenburg and Mattia Cielo and Oksana Iarygina and Franco Vazza},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.10863},
eprint = {2606.10863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.10863},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Isochrones in primordial magnetic field evolution
AU - Axel Brandenburg
AU - Mattia Cielo
AU - Oksana Iarygina
AU - Franco Vazza
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2606.10863
UR - https://arxiv.org/abs/2606.10863
AB - In the early universe, a primordial magnetic field undergoes a turbulent decay while its length scale increases due to an inverse cascade. The size of the largest processed eddy scales with the Alfvén speed and grows with time. In a diagram of Alfvén speed vs.\ length scale, all possible solutions must lie on a line through the origin with a slope proportional to the inverse of the present time. In principle, however, such lines can also be defined for earlier times. The lines for earlier times form isochrones that may be observationally accessible, for example through the magnetically driven stochastic gravitational wave background. However, the position and slope of these isochrones is sensitive to the zero point of the time. Here, we show that for any initial magnetic field, a proper time can be determined such that the resulting isochrones at early times are nearly parallel to those at late times, i.e., they have the same slope. We use two-dimensional numerical simulations of decaying MHD turbulence and vary the initial position of the peak of the magnetic energy spectrum. In this case, the evolution is governed by the conservation of anastrophy. A fit to the Alfvén time yields an accurate estimate of the factor by which the decay time is longer than the Alfvén time, while the offset in the fit provides an estimate of the proper time that needs to be added to the nominal time since the beginning of each simulation. We also find that the presence of an initial velocity field of realistic strength helps producing a more straight track from the beginning. The magnetic field parameters lie on universal isochrones even for early times. They provide a testable framework for magnetic fields generated at times as early as the end of inflation, starting with the time of reheating.
ER -