Two Cosmological Histories in a New Exponential Infrared f(T) Teleparallel Gravity: Implications for the Hubble Tension and the Low-ℓ Planck TT--EE Tension
Abstract
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 ΛCDM 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 As and τ reio for the Planck-only dataset. We show that this bimodality originates from the tension between the low-ℓ TT and EE likelihoods, which becomes pronounced in models exhibiting a significantly enhanced late ISW contribution relative to the ΛCDM 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 H0=73.43±0.69 km s−1 Mpc−1 for the Planck-only dataset and H0=72.55±0.32 km s−1 Mpc−1 after including DESI, substantially alleviating the Hubble tension. Although this branch provides a slightly better fit than ΛCDM for Planck-only data, the addition of background observations reverses this preference in favor of the standard ΛCDM 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.
Related
- Testing Extended Exponential Infrared Teleparallel Gravity with CMB, DESI, and PantheonPlus
- A Six-Parameter Teleparallel Cosmology Beyond ΛCDM: Sign-Changing Torsional Dark Energy and Implications for H0
- BAQARO: Tracing Stochastic Black Hole Growth Histories and Quasar Lightcurves in a Cosmological Context
- Untangling Similarities and Differences in Star Formation Histories Across Cosmological Simulations
- Unification of polynomial and exponential cosmological attractors
BibTeX
@misc{bedair2026cosmological,
title = {{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}},
author = {Mohamed bedair},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23956},
eprint = {2610.23956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23956},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two Cosmological Histories in a New Exponential Infrared f(T) Teleparallel Gravity: Implications for the Hubble Tension and the Low-ℓ Planck TT--EE Tension
AU - Mohamed bedair
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.23956
UR - https://arxiv.org/abs/2610.23956
AB - 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 ΛCDM 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-ℓ TT and EE likelihoods, which becomes pronounced in models exhibiting a significantly enhanced late ISW contribution relative to the ΛCDM 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±0.69 km s^−1 Mpc^−1 for the Planck-only dataset and H_0=72.55±0.32 km s^−1 Mpc^−1 after including DESI, substantially alleviating the Hubble tension. Although this branch provides a slightly better fit than ΛCDM for Planck-only data, the addition of background observations reverses this preference in favor of the standard ΛCDM 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.
ER -