  Stochastic gravitational wave background (SGWB) is a promising tool to probe
the very early universe where the standard model of particle physics and
cosmology are connected closely. As a possible component of SGWB, gravitational
waves (GW) from bubble collisions during the first order cosmological phase
transitions deserve comprehensive analyses. In 2017, Ryusuke Jinno and Masahiro
Takimoto proposed an elegant analysis approach to derive the analytical
expressions of energy spectra of GW from bubble collisions in Minkowski
spacetime avoiding large-scale numerical simulations for the first time[26].
However, they neglect the expansion of the universe and regard the duration of
phase transitions as infinity in their derivation which could deviate their
estimations from true values. For these two reasons, we give a new expression
of GW spectra by adopting their method, switching spacetime background to FLRW
spacetime, and considering a finite duration of phase transitions. By denoting
$\sigma$ as the fraction of the speed of phase transitions to the expansion
speed of the universe, we find when $\sigma$ is around $\mathcal{O}(10)$, the
maxima of estimated GW energy spectra drop by around 1 order of magnitude than
the results given by their previous work. Even when $\sigma=100$, the maximum
of GW energy spectrum is only $65\%$ of their previous estimation. Such a
significant decrease may bring about new challenges for the detectability of GW
from bubble collisions. Luckily, by comparing new spectra with PLI
(\textit{power-law integrated}) sensitivity curves of GW detectors, we find
that the detection prospect for GW from bubble collisions is still promising
for DECIGO, BBO, LISA, and TianQin in the foreseeable future.
