Cosmological electromagnetic hopfions

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 $t\rightarrow τ=\int dt/a$, where $a=a(t)$ is the scale factor of the Universe described by the Friedman-Lemaître-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.

Figures (2)

• Figure 1: Evolution of hopfion \ref{['hopfionsolu']} of field lines ${\bf D}$ in different cosmological settings. (a) For $t=0$. (b) For $t/t_0=1/2$, flat spacetime hopfion (red), radiation-dominated hopfion (blue), matter-dominated hopfion (green), and dark-energy cosmological hopfion (yellow). (c) For $t/t_0=1$ (same colors).
• Figure 2: Cosmological time dependence of the electromagnetic wavepacket spreding with respect to its flat spacetime counterpart. Red line is for flat spacetime scenario. Blue and green lines are the faster spreading induced by the radiation-dominated and matter-dominated cosmologies, respectively. Yellow lines are for a Universe with dark energy content.