Cosmological electromagnetic hopfions

TL;DR

This paper demonstrates that null electromagnetic field knots, including Hopfions, can be adapted to cosmological settings by incorporating the universe's expansion, revealing faster evolution of these structures in cosmological models.

Contribution

It extends flat spacetime electromagnetic knotted solutions to FLRW cosmologies, showing their persistence and altered dynamics in an expanding universe.

Findings

Electromagnetic Hopfions evolve faster in cosmological scenarios.

Knotted solutions in flat spacetime can be adapted to FLRW cosmology.

Implications vary across different cosmological models.

Abstract

It is shown that any mathematical solution for null electromagnetic field knots in flat spacetime is also a null field knotted solution for cosmological electromagnetic fields. This is obtained by replacing the time $t\rightarrow \tau=\int dt/a$, where $a=a(t)$ is the scale factor of the Universe described by the Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmology, and by adequately rewriting the (empty flat spacetimes) electromagnetic fields solutions in a medium defined by the FLRW metric. We found that the dispersion (evolution) of electromagnetic Hopfions is faster on cosmological scenarios. We discuss the implications of these results for different cosmological models.