Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions

TL;DR

This work develops electromagnetic-source cosmological solutions within the teleparallel $F(T)$ gravity framework for TRW spacetimes with all spatial curvatures $k\in\{-1,0,1\}$. By solving the symmetric teleparallel field equations and imposing EM conservation and energy conditions, it derives explicit $F(T)$ forms: a double power-law structure for the flat case $k=0$ and analytic, Heun-function–type or polynomial forms for the curved cases $k=\pm1$ in various expansion regimes. The results yield expressions for the EM energy density $\rho_{em}(T)$ and the fields $E(T)$, $B(T)$, linking them to the torsion scalar and scale factor, and they discuss Maxwell consistency and possible plasma cosmology implementations. The paper also outlines observational data guidelines (DESI, BAO, $H(z)$) to test and constrain these EM contributions to cosmic evolution, setting the stage for future data-driven analyses. Overall, it provides a mathematically concrete framework to quantify electromagnetic effects in expanding teleparallel cosmologies.

Abstract

We investigate the teleparallel Robertson--Walker (TRW) $F(T)$-gravity solutions for a cosmological electromagnetic source in the current paper. We use and solve the TRW $F(T)$-gravity field equations (FEs) for each value of the $k$-parameter $(-1,\,0,\,+1)$ and the electromagnetic equivalent of the equation of state (EoS), leading to new teleparallel $F(T)$ solutions. For the $k=0$ cosmological case, we find new teleparallel $F(T)$ solutions for any scale factor $n$. For $k=\pm 1$ cosmological cases, we find exact and far-future approximated new teleparallel $F(T)$ solutions for slow, linear, fast and infinitely fast universe expansion summarized by analytical functions. All the new solutions are relevant for future cosmological applications, implying any electromagnetic source processes, such as the cosmological plasma models.

Figures (1)

• Figure 1: Plot of teleparallel $F(T)$ solutions for $k=0$ and $\pm 1$ (left: $n=\frac{1}{2}$, right: $n=1$, and bottom: $n=2$. Curves are for $F_1=F_2=2F_0$ setting).