Bayesian analysis of $f(T)$ gravity using $f{\sigma }_8$ data

We use observational data from Supernovae (SNIa) Pantheon sample, from direct Hubble constant measurements with cosmic chronometers (CC), from the Cosmic Microwave Background shift parameter ${\text{CMB}}_{\text{shift}}$, and from redshift space distortion ($f{\sigma }_8$) measurements, in order to constrain $f(T)$ gravity. We do not follow the common $\gamma$ parameterization within the semi-analytical approximation of the growth rate, in order to avoid model-dependent uncertainties. Up to our knowledge this is the first time that $f(T)$ gravity is analyzed within a Bayesian framework, and with background and perturbation behaviour considered jointly. We show that all three examined $f(T)$ models are able to describe adequately the $f{\sigma }_8$ data. Furthermore, applying the Akaike, Bayesian and Deviance Information Criteria, we conclude that all considered models are statistically equivalent, however the most efficient candidate is the exponential model, which additionally presents a small deviation from $\mathrm{\Lambda }$CDM paradigm.