# New classes of modified teleparallel gravity models

## TL;DR

This paper introduces the most general second order teleparallel gravity theories based on torsion components, unifying various models and analyzing their conformal properties, including connections to general relativity and $f(R)$ gravity.

## Contribution

It formulates a comprehensive class of modified teleparallel gravity models using torsion irreducible components, encompassing known theories and exploring their Einstein frame properties.

## Key findings

- Recovery of known theories like $f(T)$ and new general relativity
- Identification of theories with Einstein frame as teleparallel equivalent of GR or $f(R)$ gravity
- Inclusion of boundary term $B$ linking torsion and Ricci scalar

## Abstract

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$ and $T_{\rm vec}$ are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or $f(T)$ gravity. Additionally, the boundary term $B$ which connects the Ricci scalar with the torsion scalar via $R=-T+B$ can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or $f(-T+B)=f(R)$ gravity, as expected.