Effect of density fluctuations on gravitational wave production in
  first-order phase transitions
  We study the effect of density perturbations on the process of first-order
phase transitions and gravitational wave production in the early Universe. We
are mainly interested in how the distribution of nucleated bubbles is affected
by fluctuations in the local temperature. We find that large-scale density
fluctuations ($H_* < k_* < \beta$) result in a larger effective bubble size at
the time of collision, enhancing the produced amplitude of gravitational waves.
The amplitude of the density fluctuations necessary for this enhancement is
${\cal P}_\zeta (k_*) \gtrsim (\beta / H_*)^{-2}$, and therefore the
gravitational wave signal from first-order phase transitions with relatively
large $\beta / H_*$ can be significantly enhanced by this mechanism even for
fluctuations with moderate amplitudes.
