Two Cosmological Histories in a New Exponential Infrared $f(T)$ Teleparallel Gravity: Implications for the Hubble Tension and the Low-$\ell$ Planck TT--EE Tension

We investigate a particular case of the New Exponential Infrared $f(T)$ teleparallel gravity model with the same number of free parameters as the standard $Λ$CDM model. Remarkably, due to the two real branches of the Lambert function $W$, the model admits two distinct cosmological solutions, denoted by $f^{(I)}$CDM and $f^{(II)}$CDM. The former exhibits a late-time phantom crossing, whereas the latter predicts an effective dark-energy density evolving from negative to positive values. Using a Markov Chain Monte Carlo analysis of the Planck CMB, DESI BAO, and Type Ia supernova data, we find that the $f^{(II)}$CDM branch develops a bimodal posterior distribution in the primordial parameters $A_s$ and $τ_{ reio}$ for the Planck-only dataset. We show that this bimodality originates from the tension between the low-$\ell$ TT and EE likelihoods, which becomes pronounced in models exhibiting a significantly enhanced late ISW contribution relative to the $Λ$CDM model. Moreover, the inclusion of background observations drives this branch toward cosmologically unacceptable parameter values, rendering it observationally unviable. The $f^{(I)}$CDM branch, on the other hand, remains observationally viable, yielding $H_0=73.43\pm0.69~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ for the Planck-only dataset and $H_0=72.55\pm0.32~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ after including DESI, substantially alleviating the Hubble tension. Although this branch provides a slightly better fit than $Λ$CDM for Planck-only data, the addition of background observations reverses this preference in favor of the standard $Λ$CDM model. These results show that the cosmological viability of this model critically depends on the choice of the Lambert $W$ branch, with only the $f^{(I)}$CDM solution remaining compatible with current cosmological observations.

Source: arXiv:2610.23956v1 - http://arxiv.org/abs/2610.23956v1 PDF: https://arxiv.org/pdf/2610.23956v1 Original Link: http://arxiv.org/abs/2610.23956v1