Data-driven reconstruction of the late-time cosmic acceleration with f(T) gravity

Abstract We use a combination of observational data in order to reconstruct the free function of f ( T ) gravity in a model-independent manner. Starting from the data-driven determined dark-energy equation-of-state parameter we are able to reconstruct the f ( T ) form. The obtained function is consistent with the standard Λ CDM cosmology within 1 σ confidence level, however the best-fit value experiences oscillatory features. We parametrise it with a sinusoidal function with only one extra parameter comparing to Λ CDM paradigm, which is a small oscillatory deviation from it, close to the best-fit curve, and inside the 1 σ reconstructed region. Similar oscillatory dark-energy scenarios are known to be in good agreement with observational data, nevertheless this is the first time that such a behavior is proposed for f ( T ) gravity. Finally, since the reconstruction procedure is completely model-independent, the obtained data-driven reconstructed f ( T ) form could release the tensions between Λ CDM estimations and local measurements, such as the H 0 and σ 8 ones.