Structure formation in $f(T)$ gravity and a solution for $H_0$ tension

Abstract: We investigate the evolution of scalar perturbations in $f(T)$ teleparallel gravity and its effects on the cosmic microwave background (CMB) anisotropy. The $f(T)$ gravity generalizes the teleparallel gravity which is formulated on the Weitzenb\"ock spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. For the first time, we derive the observational constraints on the modified teleparallel gravity using the CMB temperature power spectrum from Planck's estimation, in addition to data from baryonic acoustic oscillations (BAO) and local Hubble constant measurements. We find that a small deviation of the $f(T)$ gravity model from the $\Lambda$CDM cosmology is slightly favored. Besides that, the $f(T)$ gravity model does not show tension on the Hubble constant that prevails in the $\Lambda$CDM cosmology. It is clear that $f(T)$ gravity is also consistent with the CMB observations, and undoubtedly it can serve as a viable candidate amongst other modified gravity theories.