Modified Teleparallel $f(T)$ Gravity, DESI BAO and the $H_0$ Tension

TL;DR

This paper assesses whether late-time modifications in $f(T)$ gravity can alleviate the $H_0$ tension. By analyzing three representative $f(T)$ parametrisations against Pantheon+ SN, DESI DR2 BAO, Planck CMB distance priors, and RSD data, it links the background expansion to structure growth through an effective torsional fluid with a dynamical equation of state $w_T(z)$ and an effective gravitational coupling $G_{ m eff}$. The results show two models that push $H_0$ toward local measurements at the expense of higher tensions in matter density and clustering, and a third that shifts $H_0$ in the opposite direction; overall, the minimal $f(T)$ extensions are not favored over $\Lambda$CDM by the full dataset. This demonstrates that while late-time torsional modifications can redistribute cosmological tensions between background and growth sectors, they do not provide a complete resolution within these simple setups. The work motivates exploring more general teleparallel theories or additional degrees of freedom to address both $H_0$ and $S_8$ tensions simultaneously.

Abstract

We investigate whether late-time modifications of gravity in the teleparallel framework can impact the current tension in the Hubble constant $H_0$, focusing on $f(T)$ cosmology as a minimal and well-controlled extension of General Relativity. We consider three representative $f(T)$ parametrisations that recover the teleparallel equivalent of General Relativity at early times and deviate from it only at late epochs. The models are confronted with unanchored Pantheon+ Type~Ia supernovae, DESI DR2 baryon acoustic oscillations, compressed Planck cosmic microwave background distance priors, and redshift-space distortion data, allowing us to jointly probe the background expansion and the growth of cosmic structures. Two of the three models partially shift the inferred value of $H_0$ towards local measurements, while the third worsens the discrepancy. This behaviour is directly linked to the effective torsional dynamics, with phantom-like regimes favouring higher $H_0$ and quintessence-like regimes producing the opposite effect. A global statistical comparison shows that the minimal $f(T)$ extensions considered here are not favoured over $Λ$CDM by the combined data. Nevertheless, our results demonstrate that late-time torsional modifications can non-trivially redistribute current cosmological tensions among the background and growth sectors.

Figures (5)

• Figure 1: Cosmological background and effective sector of the $f(T)$ scenarios in comparison with $\Lambda$CDM. Left panel: Effective dark energy equation of state parameter $w_T(z)$ of the $f(T)$ models compared to $\Lambda$CDM ($w=-1$). Models 1 (crimson line) and 3 (green line) with $\lambda_1=0.36$ and $\lambda_3=0.42$ respectively, show phantom-like behaviour ($w_T<-1$), whereas Model 2 with $\lambda_2=0.09$ (blue line), lies in the quintessence regime ($w_T>-1$). Right panel: Effective Newton’s constant $G_{\mathrm{eff}}/G$ as a function of the redshift $z$. Models 1 (crimson line) and 3 (green line) with $\lambda_1=0.36,\, \lambda_3=0.42$ respectively, show $G_{\mathrm{eff}}>G$, whereas Model 2 with $\lambda_2=0.09$ (blue line) exhibits $G_{\mathrm{eff}}<G$, with distinct implications for structure formation. The black dashed line $G_{\mathrm{eff}}/G=1$ corresponds to the GR limit.
• Figure 2: Comparison of the two-dimensional posterior distributions in the $(H_0,\Omega_{\mathrm{m}0})$, $(H_0,\Omega_{\mathrm{b}0})$, and $(\Omega_{\mathrm{m}0},\Omega_{\mathrm{b}0})$ planes obtained from the individual SN, BAO, and BAO+CMB datasets. The contours correspond to the 68% and 95% confidence levels (C.L.). The top-left panel shows the results for the $\Lambda$CDM model, while the remaining panels correspond to the $f_1(T)$ (top-right), $f_2(T)$ (bottom-left), and $f_3(T)$ (bottom-right) models. The relative displacement and overlap of the contours reveal the presence of internal tensions among the datasets for each model.
• Figure 3: Two-dimensional posterior distributions in the $(\Omega_{\mathrm{m}0},S_8)$ plane obtained from the RSD dataset. The contours correspond to the 68% and 95% confidence levels (C.L.) for the $\Lambda$CDM and $f(T)$ gravity models. For reference, the Planck 2018 best-fit constraint Planck:2018vyg is also shown.
• Figure 4: Two-dimensional posterior distributions for the $\Lambda$CDM and $f(T)$ gravity models obtained from the full dataset combination (SN + BAO + CMB + RSD). The contours correspond to the 68% and 95% confidence levels (C.L.). The figure displays all one- and two-dimensional marginalised constraints among the parameters $H_0$, $\Omega_{\mathrm{m}0}$, $\Omega_{\mathrm{b}0}$, and $S_8$. Differences in the location of the contours illustrate how the various $f(T)$ parametrisations modify the joint parameter constraints relative to the $\Lambda$CDM scenario.
• Figure 5: Reconstruction of the effective dark energy equation of state parameter $w_T(z)$ for the three $f(T)$ models using the full dataset combination SN+BAO+CMB+RSD. Solid curves correspond to the best-fit reconstruction, while shaded regions represent the 68% (dark gray) and 95% (light gray) CL obtained from the MCMC analysis. The three panels correspond to: Model 1 (top-left), Model 2 (top-right), and Model 3 (bottom). Compared to Fig. \ref{['fig:theory_wde']}, which displayed representative $w_T$ evolutions for each $\lambda$ parametrisation, the results presented here incorporate the full statistical confidence intervals, demonstrating that the constraints on $w_T$ are consistently tight across all three models.