气泡超过哈勃半径情形下声学引力波的超前阶计算
Acoustic gravitational waves beyond leading order in bubble over Hubble radius
AI总结：
本文研究了宇宙学一阶相变中大气泡区域的声学引力波功率谱，通过宇宙学微扰理论展开计算，发现次领先阶的三个新贡献会抑制引力波峰值振幅，并提供了相应的解析近似与跨频率平滑连接方法。
摘要：
我们计算了宇宙学一阶相变中声波产生的引力波功率谱，研究的是尚未探索的大气泡区域，即平均气泡间距 $R_*$ 是哈勃长度 $\mathcal{H}_*^{-1}$ 的不可忽略分数，即 $R_*\mathcal{H}_* \lesssim \mathcal{O}(1)$。由于引力波信号振幅随 $R_*\mathcal{H}_*$ 增加而增大，这也是大信号区域。在此区域中，此前被忽略的引力效应变得重要。我们在宇宙学微扰理论框架下进行计算，以参数 $R_*\mathcal{H}_*$（即气泡超过哈勃半径）为展开量。领先阶项是声学引力波产生的标准结果。在次领先阶，我们发现了三个新贡献：两个贡献来自声波和引力波动力学的广义相对论修正。第三个贡献来自曲率扰动诱导的引力波。这些贡献抑制了引力波峰值振幅。相对于领先阶贡献，抑制因子按 $(R_*\mathcal{H}_*)^2$ 标度，并依赖于其他相变参数，如声速 $c_s$、声学源持续时间以及速度场峰值波数 $k_p$。在速度场的简化模型中，我们发现当 $R_*\mathcal{H}_* \simeq 0.5$ 时，抑制因子介于 $2\\%$ 至 $15\\%$ 之间，但与流体均方根速度无关。我们提供了次领先阶修正的解析近似，以及在不同频率区域间平滑连接的方法。我们的工作提高了当前对大气泡相变这一相对未探索区域中引力波功率谱估算的精度。
英文摘要：
We calculate the gravitational wave power spectrum from sound waves in a cosmological first order phase transition in the unexplored regime of large bubbles, by which we mean that the mean bubble spacing $R_*$ is a non-negligible fraction of the Hubble length $\mathcal{H}_*^{-1}$, i.e. $R_*\mathcal{H}_* \lesssim \mathcal{O}(1)$. Since the amplitude of the gravitational wave signal increases with $R_*\mathcal{H}_*$, this is also the loud signal regime. In this regime the effects of gravity, hitherto neglected, become relevant. We carry out the calculation in cosmological perturbation theory expanding in the parameter $R_*\mathcal{H}_*$, or bubble over Hubble radius. The leading order term is the standard result for acoustic production of gravitational waves. At next-to-leading order we find three novel contributions: two contributions arise from general relativistic corrections to the dynamics of both sound and gravitational waves. A third contribution comes from gravitational waves induced by curvature perturbations. These contributions suppress the gravitational wave peak amplitude. The suppression factor, with respect to the leading order contribution, scales as $(R_*\mathcal{H}_*)^2$, and also depends on other transition parameters, such as the sound speed $c_s$, the duration of the acoustic source, and the peak wavenumber of the velocity field $k_p$. In a simplified model of the velocity field, we find that the suppression factor lies between $2\%$ and $15\%$ when $R_*\mathcal{H}_* \simeq 0.5$, but is independent of the root mean squared fluid velocity. We provide analytical approximations to the next-to-leading order corrections, and a recipe to join them smoothly across different frequency regimes. Our work improves the precision of the current estimations of the gravitational wave power spectrum in the relatively unexplored regime of phase transition with large bubbles.
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