# The effective field theory approach of teleparallel gravity, $f(T)$ gravity and beyond

## TL;DR

This paper develops an effective field theory framework for torsional modified gravity, especially $f(T)$ gravity, enabling systematic analysis of background and perturbations, and applies it to cosmological models to derive observational constraints.

## Contribution

It generalizes the effective field theory approach to torsional gravity and applies it to $f(T)$ models, deriving new parameters for observational tests.

## Key findings

- Derived expressions for Newtonian constant and PPN parameter $b$ in $f(T)$ gravity.
- Analyzed scalar perturbations up to second order in $f(T)$ models.
- Introduced a new parameter quantifying deviations from general relativity, useful for observational constraints.

## Abstract

We develop the effective field theory approach to torsional modified gravities, a formalism that allows for the systematic investigation of the background and perturbation levels separately. Starting from the usual effective field theory approach to curvature-based gravity, we suitably generalize it at the background level by including terms of the contracted torsion tensor, and at the perturbation level by including pure torsion perturbative terms and mixed perturbative terms of torsion and curvature. Having constructed the effective field theory action of general torsional modified gravity, amongst others we focus on $f(T)$ gravity and we perform a cosmological application. We investigate the scalar perturbations up to second order, and we derive the expressions of the Newtonian constant and the post Newtonian parameter $\gamma$. Finally, we apply this procedure to two specific and viable $f(T)$ models, namely the power-law and the exponential ones, introducing a new parameter that quantifies the deviation from general relativity and depends on the model parameters. Since this parameter can be expressed in terms of the scalar perturbation mode, a precise measurement of its evolution could be used as an alternative way to impose constraints on $f(T)$ gravity and break possible degeneracies between different $f(T)$ models.