arXiv 2008.136932020-08-28hep-thgr-qc

高次谐波回路的尖点特性

The cusp properties of High Harmonic Loops

Despoina Pazouli, Anastasios Avgoustidis, Edmund J. Copeland

备注：: 17 pages, 8 figures
发表信息：: Phys. Rev. D 103, 063536 (2021)
DOI：: 10.1103/PhysRevD.103.063536

摘要：

在从宇宙弦环网络中确定尖点的引力信号时，必须假设一些关键参数。这些包括每周期的弦振荡的尖点的典型数量和在尖点事件处评估的弦上的左和右移动波的锐度参数的典型值。这两点都很重要，因为储存在从弦环发射的引力波中的能量与每个周期的尖点数量成正比，与弦上左右移动模式相关的锐度参数的乘积成反比。在适当的单位中，这两个量通常被认为是统一的。为了尝试把这些参数放在一个更坚实的基础上，我们详细分析了大量随机选择的弦环，这些弦环可能有与之相关的高次谐波，比如人们可能期望在早期宇宙中切断无限弦而形成的。这使我们能够分析成千上万的循环，并获得这些关键参数的详细统计数据。虽然我们发现，一般来说，锐度参数确实接近于1，如在以前的工作中所假设的那样（偶尔例外，它们可能变成$O(10^{-2})$），但每个周期的尖点数量直接与环路上的谐波数量成比例，并且可能显著大于1。这就有可能产生比预期更大的信号，从而有可能导致无量纲宇宙弦张力$Gμ$的更紧边界。

英文摘要：

In determining the gravitational signal of cusps from a network of cosmic strings loops, a number of key parameters have to be assumed. These include the typical number of cusps per period of string oscillation and the typical values of the sharpness parameters of left and right moving waves on the string, evaluated at the cusp event. Both of these are important, as the power stored in the gravitational waves emitted from the loops of string is proportional to the number of cusps per period, and inversely proportional to the product of the sharpness parameters associated with the left and right moving modes on the string. In suitable units both of these quantities are usually thought to be of order unity. In order to try and place these parameters on a more robust footing, we analyse in detail a large number of randomly chosen loops of string that can have high harmonics associated with them, such as one might expect to form by chopping off an infinite string in the early universe. This allows us to analyse tens of thousands of loops and obtain detailed statistics on these crucial parameters. While we find in general the sharpness parameters are indeed close to unity, as assumed in previous work (with occasional exceptions where they can become $O(10^{-2})$), the cusp number per period scales directly with the number of harmonics on the loop and can be significantly larger than unity. This opens up the possibility of larger signals than would have otherwise been expected, potentially leading to tighter bounds on the dimensionless cosmic string tension $Gμ$.

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