Dynamical stability of 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 $f_T(0,0)<0$, $f_{T_G{T}_G}>0$. We apply these restrictions for the few types of functions discussed by the early authors.

some results was corrected, journal's ref. was added

References in corpus (9)

• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• The teleparallel equivalent of general relativity
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Dynamical behavior in $f(T,T_G)$ cosmology
• Cosmological applications of $F(T,T_G)$ gravity
• Dynamical features of scalar-torsion theories
• Conformal Invariant Teleparallel Cosmology

Cited by in corpus (8)

• Teleparallel Gravity: From Theory to Cosmology
• Cosmological bouncing solutions in f(T,B) gravity
• Bounce Models within Teleparallel modified gravity
• Asymptotic cosmological regimes in scalar-torsion gravity with a perfect fluid
• Bianchi I cosmological solutions in teleparallel gravity
• Spin connection and cosmological perturbations in $f(T)$ gravity
• Spin connection and cosmological perturbations in scalar-torsion gravity
• Stability in higher-derivative matter fields theories