Hubble Constant, <i>S</i> 8, and Sound Horizon Tensions: A Study Within the Teleparallel Framework

Abstract Increasingly precise cosmological observations have revealed subtle yet persistent discrepancies, collectively known as cosmological tensions. Despite the success of the standard $\Lambda$CDM model in describing the evolution of the universe, growing tensions between early- and late-time cosmological observations, such as those involving the Hubble constant and matter clustering amplitude, suggest the potential need for new physics beyond the concordance model. In this work, we have analyzed the $H_0$, $S_8$, and $r_d$ tensions within the teleparallel framework. To do so, we propose a model where the matter is minimally coupled as an inverse term with the torsion scalar. Our analysis demonstrates that the inverse torsion term primarily impacts the late-time expansion, shifting the inferred $H_0$, while the $\mathcal {T}$ coupling modifies structure growth, reducing the $S_8$ tension. Through joint analyses with DESI, GW, CC, and Union3 data, we show that this $f(T,\mathcal {T})$ model can statistically compete with $\Lambda$CDM ($\Delta \chi ^2 \lesssim 2$), while offering distinct physical insights into the origin of the observed cosmological tensions. Our findings not only shed light on the possible alleviation of existing cosmological tensions but also reinforce the consistency of the universe’s late-time accelerated expansion and its dynamical transition history.