Cosmic string loop production functions
Cosmic string loop production functions
复制标题
宇宙弦循环产生函数
DOI：
10.1088/1475-7516/2019/06/015
复制
发表时间：
2019
影响因子：
6.4
通讯作者：
D. Steer
中科院分区：
文献类型：
--
作者：
P. Auclair;C. Ringeval;M. Sakellariadou;D. Steer
对膨胀宇宙中南部-后岛宇宙弦的数值模拟表明，环分布松弛到通用配置，即所谓的标度制度，在大尺度上呈幂律形状。然而，幂律指数的精确估计仍然存在争议，而数值模拟并未包含预计会影响小规模网络动态的所有辐射和逆反应效应。通过使用玻尔兹曼方法，我们表明循环产生函数相对于循环大小的陡度与宇宙循环分布的剧烈变化相关。对于 a(t) ∝ tν 变化的比例因子，我们发现亚临界循环产生函数具有 Polchinski-Rocha 指数 χ < (3 ν − 1)/2，产生的比例循环分布大多对宇宙弦网络的红外 (IR) 和紫外 (UV) 假设不敏感。对于这些，根据之前的结果，宇宙学预测预计将相对稳健。相反，具有 χ ≥ (3ν−1)/2 的临界和超临界环路产生函数被证明是依赖于红外物理的，这通常会阻止环路分布松弛到缩放。在后一种情况下，我们讨论了收敛所需的额外正则化，并表明，尽管仍然可以达到缩放机制，但与天真的期望相比，宇宙环分布的形状已被修改。最后，我们讨论我们的研究结果的含义。
Numerical simulations of Nambu-Goto cosmic strings in an expanding universe show that the loop distribution relaxes to an universal configuration, the so-called scaling regime, which is of power law shape on large scales. Precise estimations of the power law exponent are, however, still matter of debate while numerical simulations do not incorporate all the radiation and backreaction effects expected to affect the network dynamics at small scales. By using a Boltzmann approach, we show that the steepness of the loop production function with respect to loops size is associated with drastic changes in the cosmological loop distribution. For a scale factor varying as a(t) ∝ tν, we find that sub-critical loop production functions, having a Polchinski-Rocha exponent χ < (3 ν − 1)/2, yield scaling loop distributions which are mostly insensitive to infra-red (IR) and ultra-violet (UV) assumptions about the cosmic string network. For those, cosmological predictions are expected to be relatively robust, in accordance with previous results. On the contrary, critical and super-critical loop production functions, having χ ≥ (3ν−1)/2, are shown to be IR-physics dependent and this generically prevents the loop distribution to relax towards scaling. In the latter situation, we discuss the additional regularisations needed for convergence and show that, although a scaling regime can still be reached, the shape of the cosmological loop distribution is modified compared to the naive expectation. Finally, we discuss the implications of our findings.