$H_0$ Tension and the Phantom Regime: A Case Study In Terms of an Infrared $f(T)$ Gravity

Abstract

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 $z \lesssim 2$.