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

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