Dynamical stability of extended teleparallel gravity

TL;DR

This paper investigates the stability of extended teleparallel gravity theories with a function of torsion scalar and Gauss-Bonnet analogue, deriving conditions for Minkowski space stability and analyzing specific functional forms.

Contribution

It introduces stability criteria for $f(T,T_G)$ gravity, extending previous teleparallel models by including higher derivative terms and analyzing their implications.

Findings

Stability requires $f_T(0,0)<0$ and $f_{T_GT_G}>0$.

Derived explicit stability conditions for specific $f(T,T_G)$ functions.

Identified potential instabilities due to higher derivatives in extended teleparallel gravity.

Abstract

We discuss modified teleparallel gravity with function $f(T,T_G)$ in the action, where function depend on two arguments: torsion scalar $T$ and analogue of Gauss-Bonnet invariant $T_G$. In contradistinction to usual teleparallel gravity $f(T)$, this theory contains higher derivative terms, which may produce different instabilities. We discuss Minkowski stability problem in such kind of theories and explicitly demonstrate that for stability must be $f_T(0,0)<0$, $f_{T_GT_G}>0$. We apply these restrictions for the few types of functions discussed by the early authors.