  We investigate the gravitational wave spectrum resulted from the cosmological
first-order phase transition. We compare two models; one is a scalar field
model without gravitation, while the other is a scalar field model with
gravitation. Based on the sensitivity curves of the LISA space-based
interferometer on the stochastic gravitational-wave background, we compare the
difference between the gravitational wave spectra of the former and the latter
cases resulted from the bubble collision process. Especially, we calculated the
speed of the bubble wall before collision for the two models numerically. We
show that the difference between the amplitudes of those spectra can clearly
distinguish between the two models. We expect that the LISA with Signal to
Noise Ratio =10 could observe the spectrum as the fast first-order phase
transition.
