  Gravitational waves (GWs) are useful to test gravitational theories and to
probe the physics in the early universe. In this paper, we investigate the
scalar induced gravitational waves (SIGWs) in symmetric teleparallel gravity
with a parity-violating term. The presence of the parity-violating term leads
to the velocity birefringence effect of the SIGWs. However, after taking into
account the observational constraints on the speed of GWs, the contribution
from the parity-violating term to SIGWs is negligible. Nevertheless, the
contribution to SIGWs from the perturbations of the connection can be
significant, and results in a multipeak structure in the energy density of
SIGWs. This feature makes the symmetric teleparallel gravity distinguishable
from the general relativity.
