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We establish new constraints on $f(T)$ gravity models by using cosmologicaldata. In particular, we investigate the restrictions given by the gas massfraction measurements of galaxy clusters and transversal BAO data. Both datasets are regarded as weakly dependent on a fiducial cosmology. In addition, wealso include a CMB measurement of the temperature power spectrum first peak,along with $H(z)$ values from cosmic chronometers and supernovae data from thePantheon data set. We also perform a forecast for future constraints on thedeviation of $f(T)$ models from the $\Lambda$CDM scenario by following thespecifications of the J-PAS and Euclid surveys and find significantimprovements on the constraints of the $b$-parameter, when compared to theresults of the statistical analysis.

Observational Constraints on $f(T)$ Gravity from Model-Independent Data