Gravitational waves induced by scalar perturbations with a lognormal peak
Gravitational waves induced by scalar perturbations with a lognormal peak
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DOI：
10.1088/1475-7516/2020/09/037
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发表时间：
2020-05
影响因子：
6.4
通讯作者：
Shi Pi;Misao Sasaki
中科院分区：
文献类型：
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作者：
Shi Pi;Misao Sasaki
我们研究了由原初标量扰动引起的随机引力波（GW）背景，其频谱在 k=k* 处具有宽度 Δ 的对数正态峰值。我们推导出窄峰 (Δ≪1) 和宽峰 (Δ≳ 1) 的 GW 谱 ΩGW 的分析公式。在窄峰情况下，光谱具有双峰特征，在 k= 2k*/√3 处具有更尖锐的峰。在光谱的红外 (IR) 侧，我们发现幂律行为在幂律指数 k=kb 处出现中断，从远红外侧的 k3 变为近红外侧的 k2。我们发现转折频率与峰值频率的比率由 Δ 决定，即 fb/fp≈√3Δ，其中 fb 和 fp 分别是转折频率和峰值频率。在宽峰情况下，我们发现引力波谱在 k=k* 处也有一个对数正态峰，但 Δ/√2 宽度较小。使用这些导出的分析公式，我们还提出了狭义和广义情况下 ΩGW 最大值的表达式。我们的结果将为未来几十年寻找诱导引力波信号提供有用的工具。
We study the stochastic gravitational wave (GW) background induced by the primordial scalar perturbation with the spectrum having a lognormal peak of width Δ at k=k*. We derive an analytical formula for the GW spectrum ΩGW for both narrow (Δ≪1) and broad (Δ≳ 1) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at k= 2k*/√3. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at k=kb in the power-law index where it chages from k3 on the far IR side to k2 on the near IR side. We find the ratio of the break frequency to the peak frequency is determined by Δ as fb/fp≈√3Δ, where fb and fp are the break and peak frequencies, respectively. In the broad-peak case, we find the GW spectrum also has a lognormal peak at k=k* but with a smaller width of Δ/√2. Using these derived analytic formulae, we also present expressions for the maximum values of ΩGW for both narrow and broad cases. Our results will provide a useful tool in searching for the induced GW signals in the coming decades.