A Self-Consistent Hubble Expansion in f(T) Gravity model: Confrontation with Recent Observations

TL;DR

This paper develops a self-consistent anisotropic $f(T)$ gravity model with an exponential form, tests it against recent cosmological data, and finds it can explain cosmic acceleration without dark energy.

Contribution

It introduces a novel anisotropic $f(T)$ gravity model with a self-consistent Hubble function derived from field equations, validated by multiple observational datasets.

Findings

Model fits observational data well, with $H_0$ between 70-73 km/s/Mpc.

Reproduces supernovae and gravitational-wave luminosity distances accurately.

Can explain cosmic acceleration without dark energy.

Abstract

The accelerated expansion of the universe remains one of the most profound puzzles in modern cosmology, often attributed to dark energy within the framework of General Relativity. As an alternative, modified teleparallel gravity theories such as $f(T)$ gravity offer a purely geometric mechanism to explain cosmic acceleration. In this work, we construct a plane-symmetric anisotropic cosmological model in the framework of exponential $f(T)$ gravity, adopting the functional form $f(T) = T + u e^{-vT}$. A key novelty of this study is that the Hubble function $H(z)$ is derived self-consistently from the field equations rather than being prescribed phenomenologically. Furthermore, we provide the first comprehensive observational test of an anisotropic $f(T)$ model using a combination of DESI, gravitational-wave (GW) data, and complementary datasets including OHD, CMB, and Pantheon+SH0ES. Our best-fit analysis yields $70 \lesssim H_0 \lesssim 73~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $0.28 \lesssim \Omega_m \lesssim 0.34$, and $-0.99 \lesssim \omega \lesssim -0.69$, all consistent with current late-time cosmological observations. The model accurately reproduces the distance modulus of Type Ia supernovae and the luminosity-distance relation from gravitational-wave standard sirens. These results demonstrate that the proposed anisotropic exponential $f(T)$ model can account for the observed cosmic acceleration without invoking a dark-energy component, thereby offering a novel and observationally consistent framework for studying anisotropic extensions of gravity.