Gravitational waves from bubble dynamics: Beyond the Envelope
  We study gravitational-wave production from bubble dynamics (bubble
collisions and sound waves) during a cosmic first-order phase transition with
an analytic approach. We first propose modeling the system with the thin-wall
approximation but without the envelope approximation often adopted in the
literature, in order to take bubble propagation after collisions into account.
The bubble walls in our setup are considered as modeling the scalar field
configuration and/or the bulk motion of the fluid. We next write down analytic
expressions for the gravitational-wave spectrum, and evaluate them with
numerical methods. It is found that, in the long-lasting limit of the collided
bubble walls, the spectrum grows from $\propto f^3$ to $\propto f^1$ in low
frequencies, showing a significant enhancement compared to the one with the
envelope approximation. It is also found that the spectrum saturates in the
same limit, indicating a decrease in the correlation of the energy-momentum
tensor at late times. We also discuss the implications of our results to
gravitational-wave production both from bubble collisions (scalar dynamics) and
sound waves (fluid dynamics).
