Gravitational Waves in Modified Teleparallel Theories
  We investigate the gravitational waves and their properties in various
modified teleparallel theories, such as $f(T), f(T,B)$ and $f(T,T_G)$
gravities. We perform the perturbation analysis both around a Minkowski
background, as well as in the case where a cosmological constant is present,
and for clarity we use both the metric and tetrad language. For $f(T)$ gravity
we verify the result that no further polarization modes comparing to general
relativity are present at first-order perturbation level, and we show that in
order to see extra modes one should look at third-order perturbations. For
non-trivial $f(T,B)$ gravity, by examining the geodesic deviation equations, we
show that extra polarization models, namely the longitudinal and breathing
modes, do appear at first-order perturbation level, and the reason for this
behavior is the fact that although the first-order perturbation does not have
any effect on $T$, it does affect the boundary term $B$. Finally, for
$f(T,T_G)$ gravity we show that at first-order perturbations the gravitational
waves exhibit the same behavior to those of $f(T)$ gravity. Since different
modified teleparallel theories exhibit different gravitational wave properties,
the dvancing gravitational-wave astronomy would help to alleviate the
degeneracy not only between curvature and torsional modified gravity but also
between different subclasses of modified teleparallel gravities.
