气泡碰撞产生的引力波：解析推导
Gravitational waves from bubble collisions: analytic derivation
摘要：
本文研究了宇宙学一级相变过程中气泡碰撞产生的引力波。在文献中，这样的光谱已经估计通过模拟气泡动力学，在所谓的薄壁和包络近似在一个平坦的背景度量。然而，我们表明，在这些假设，引力波频谱可以估计在一个分析的方式。我们的估计是基于观察到的两点相关的能量动量张量$\langle T(x)T(y)\rangle$可以表示在这些假设下的分析。虽然光谱的最终表达式包含一些不能明确计算的积分，但我们可以很容易地用数值估计它。结果表明，气泡对相关器的贡献主要来自于气泡对相关器的贡献，并且气泡对相关器的贡献与相关器中的$f^{-1}$成正比。我们还提供了光谱的拟合公式。
英文摘要：
We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope approximations in a flat background metric. However, we show that, within these assumptions, the gravitational wave spectrum can be estimated in an analytic way. Our estimation is based on the observation that the two-point correlator of the energy-momentum tensor $\langle T(x)T(y)\rangle$ can be expressed analytically under these assumptions. Though the final expressions for the spectrum contain a few integrations that cannot be calculated explicitly, we can easily estimate it numerically. As a result, it is found that the most of the contributions to the spectrum come from single-bubble contribution to the correlator, and in addition the fall-off of the spectrum at high frequencies is found to be proportional to $f^{-1}$. We also provide fitting formulae for the spectrum.
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