Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or $\Lambda$CDM as separate scenarios. We reconstruct the $f(T)$ gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and standard model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular $f(T)$ gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.