# Bayesian analysis of $f(T)$ gravity using $f\sigma_8$ data

## TL;DR

This paper performs a Bayesian analysis of $f(T)$ gravity models using diverse cosmological data, jointly considering background and perturbation behaviors, and finds that all models fit the data well with the exponential model being most efficient.

## Contribution

First Bayesian analysis of $f(T)$ gravity with background and perturbation data considered together, avoiding model-dependent uncertainties in growth rate parameterization.

## Key findings

- All $f(T)$ models fit $f\sigma_8$ data adequately.
- Models are statistically equivalent according to information criteria.
- The exponential $f(T)$ model shows a slight deviation from $\Lambda$CDM.

## Abstract

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 $\Lambda$CDM paradigm.