$f(T)$ gravity after GW170817 and GRB170817A
  The combined observation of GW170817 and its electromagnetic counterpart
GRB170817A reveals that gravitational waves propagate at the speed of light in
high precision. We apply the effective field theory approach to investigate the
experimental consequences for the theory of $f(T)$ gravity. We find that the
speed of gravitational waves within $f(T)$ gravity is exactly equal to the
light speed, and hence the constraints from GW170817 and GRB170817A are
trivially satisfied. The results are verified through the standard analysis of
cosmological perturbations. Nevertheless, by examining the dispersion relation
and the frequency of cosmological gravitational waves, we observe a deviation
from the results of General Relativity, quantified by a new parameter. Although
its value is relatively small in viable $f(T)$ models, its possible future
measurement in advancing gravitational-wave astronomy would be the smoking gun
of testing this type of modified gravity.
