Dynamical stability of extended teleparallel gravity

We discuss modified teleparallel gravity with function f(T, T-G) in the action, where the function depends 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 it must be f(T)(0, 0) < 0, f(TGTG) > 0. We apply these restrictions for the few types of functions discussed by the early authors.