  We investigate stellar core collapse in scalar-tensor theory with a massive
self-interacting scalar field. In these theories, strong long-lived inverse
chirp signals could be induced during the stellar core collapse, which provides
us with several potential smoking-gun signatures that could be found using
current ground-based detectors. We show that the existence of self-interaction
in the potential of the scalar field can significantly suppress spontaneous
scalarization and the amplitude of the monopole gravitational-wave radiation.
Moreover, this suppression due to self-interaction is frequency dependent and
may be discernible in LIGO/Virgo's sensitive band. Therefore, self-interaction
should be considered when constraining scalar-tensor coupling parameters with
gravitational-wave detections. Alternatively, if such monopole
gravitational-wave signals are detected, then one may be able to infer the
presence of self-interaction.
