Light bending in $f(T)$ gravity

In the framework of $f(T)$ gravity, we focus on a weak-field and spherically symmetric solution for the Lagrangian $f(T)=T+\alpha T^{2}$, where $\alpha$ is a small constant which parameterizes the departure from General Relativity. In particular, we study the propagation of light and obtain the correction to the general relativistic bending angle. Moreover, we discuss the impact of this correction on some gravitational lensing observables, and evaluate the possibility of constraining the theory parameter $\alpha$ by means of observations. In particular, on taking into account the astrometric accuracy in the Solar System, we obtain that $|\alpha| \leq 1.85 \times 10^{5}\, \mathrm{m^{2}}$; this bound is looser than those deriving from the analysis of Solar System dynamics, e.g. $|\alpha| \leq 5 \times 10^{-1}\, \mathrm{m^{2}}$, $|\alpha| \leq 1.8 \times 10^{4}\, \mathrm{m^{2}}$ or $|\alpha| \leq 1.2 \times 10^{2}\, \mathrm{m^{2}}$ . However we suggest that, since the effect only depends on the impact parameter, better constraints could be obtained by studying light bending from planetary objects.