Gravitational waves from first-order phase transitions: towards model separation by bubble nucleation rate

We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum. By using the method of relating the spectrum with the two-point correlator of the energy-momentum tensor < T(x)T(y)>, we first write down analytic expressions for the spectrum with a Gaussian correction to the commonly used nucleation rate, Gamma proportional to e(beta t) -> e(beta t-gamma 2t2), under the thin-wall and envelope approximations. Then we quantitatively investigate how the spectrum changes with the size of the Gaussian correction. It is found that the spectral shape shows O(10)% deviation from Gamma proportional to e(beta t) case for some physically motivated scenarios. We also briefly discuss detector sensitivities required to distinguish different spectral shapes.