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Cosmology faces a pressing challenge with the Hubble constant ($H_0$)tension, where the locally measured rate of the Universe's expansion does notalign with predictions from the cosmic microwave background (CMB) calibratedwith $\Lambda$CDM model. Simultaneously, there is a growing tension involvingthe weighted amplitude of matter fluctuations, known as $S_{8,0}$ tension.Resolving both tensions within one framework would boost confidence in any oneparticular model. In this work, we analyse constraints in $f(T)$ gravity, aframework that shows promise in shedding light on cosmic evolution. Wethoroughly examine prominent $f(T)$ gravity models using a combination of datasources, including Pantheon+ (SN), cosmic chronometers (CC), baryonic acousticoscillations (BAO) and redshift space distortion (RSD) data. We use thesemodels to derive a spectrum of $H_0$ and $S_{8,0}$ values, aiming to gaugetheir ability to provide insights into, and potentially address, the challengesposed by the $H_0$ and $S_{8,0}$ tensions.

Growth of structures using redshift space distortion in $f(T)$ Cosmology