Cosmological viable models in $f(T,B)$ gravity as solutions to the $H_0$ tension

In this work we present a further investigation about Teleparallel Gravity Cosmology. We demonstrate that according the current astrophysical data (CC+Pantheon+BAO samplers with late universe measurements SH0ES+H0LiCOW), an $f(T,B)$ theory can provide another interpretation to the oscillatory behaviour of the dark energy equation of state when applied to late times. The four $f(T,B)$ cosmological viable models proposed here can undergo an epoch of late-time acceleration and reproduce quintessence and phantom regimes with a transition along the phantom-divided line, making this theory a good approach to modify the standard $\mathrm{\Lambda }$CDM model.