论文标题
标量扰动引起的引力波，具有对数正常峰
Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak
论文作者
论文摘要
我们研究了由原始标量扰动引起的随机引力波（GW）背景，其频谱具有宽度宽度$δ$ th $ k = k _*$。我们为narrow（$δ\ ll1 $）和宽（$δ\ gtrsim1 $）峰的GW Spectrum $ω__\ text {gw} $得出一个分析公式。在窄峰情况下，频谱具有双峰功能，较尖峰的峰值为$ k = 2k _*/\ sqrt {3} $。在频谱的红外线（IR）方面，我们在幂律索引中发现了$ k = k_b $的幂律行为，在$ k = k_b $中，它从远处的$ k^3 $搅拌到近红外线的$ k^2 $。我们发现，断裂频率与峰频率的比率由$δ$确定为$ f_b/f_p \ of of sqrt {3}δ$，其中$ f_b $和$ f_p $分别是断点和峰值频率。在宽峰情况下，我们发现GW频谱在$ k = k _*$处的对数正态峰值，但宽度较小$Δ/\ sqrt2 $。使用这些派生的分析公式，我们还为窄案例和广泛案例提供了$ω__\ text {gw} $的最大值的表达式。我们的结果将为未来几十年搜索引起的GW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 $Ω_\text{GW}$ for both narrow ($Δ\ll1$) and broad ($Δ\gtrsim1$) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at $k= 2k_*/\sqrt{3}$. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at $k=k_b$ in the power-law index where it chages from $k^3$ on the far IR side to $k^2$ on the near IR side. We find the ratio of the break frequency to the peak frequency is determined by $Δ$ as $f_b/f_p\approx\sqrt{3}Δ$, where $f_b$ and $f_p$ 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 $Δ/\sqrt2$. Using these derived analytic formulae, we also present expressions for the maximum values of $Ω_\text{GW}$ for both narrow and broad cases. Our results will provide a useful tool in searching for the induced GW signals in the coming decades.
