$H_0$ Tension and the Phantom Regime: A Case Study In Terms of an
  Infrared $f(T)$ Gravity
  We propose an $f(T)$ teleparallel gravity theory including a torsional
infrared (IR) correction. We show that the governing Friedmann's equations of a
spatially flat universe include a phantom-like effective dark energy term
sourced by the torsion IR correction. As has been suggested, this phantom phase
does indeed act as to reconcile the tension between local and global
measurements of the current Hubble value $H_0$. The resulting cosmological
model predicts an electron scattering optical depth $\tau_e\thickapprox 0.058$
at reionization redshift $z_{re} \sim 8.1$, in agreement with observations. The
predictions are however in contradiction with baryon acoustic oscillations
(BAO) measurements, particularly the distance indicators. We argue that this is
the case with any model with a phantom dark energy model that has effects
significant enough at redshifts $z \lesssim 2$ as to be currently observable.
The reason being that such a scenario introduces systematic differences in
terms of distance estimates in relation to the standard model; e.g., if the
angular diameter distance to the recombination era is to be kept constant while
$H_0$ is increased in the context of a phantom scenario, the distances there
are systematically overestimated to all objects at redshifts smaller than
recombination. But no such discrepancies exist between $\Lambda$CDM predictions
and current data for $z \lesssim 2$.
