  We investigate the cosmological perturbations around all three branches of
spatially flat universe with different connections in symmetric teleparallel
gravity. The model we consider can cover both the case of f(Q) model and that
of the non-minimal coupling between a scalar field and the non-metricity
scalar. We focus on analyzing and comparing the propagation behavior and
stability of the tensorial and non-tensorial gravitational waves on spatially
flat universe with different connections.
