arXiv 2603.048502026-03astro-ph.COgr-qchep-phhep-th

随机晶格模拟混合膨胀

STOchastic LAttice Simulation of hybrid inflation

Tokyo Metropolitan College of Industrial Technology（东京都立产业技术短期大学）；Rikkyo University（立教大学）

Tomoaki Murata, Yuichiro Tada

备注：: 23 pages, 9 figures
发表信息：: JCAP 09 (2026) 061
DOI：: 10.1088/1475-7516/2026/09/061

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AI总结：

该研究通过随机晶格模拟混合膨胀模型，分析了曲率扰动的拓扑结构及其对早期宇宙物理的探测意义。

摘要：

我们研究了多瀑布混合膨胀模型中产生的曲率扰动的空间分布，这些模型已知会产生各种拓扑缺陷。使用基于膨胀随机形式的晶格模拟代码STOLAS，我们分析了六个案例，通过改变瀑布场数量n和inflaton势能函数的形式（“二次”和“三次”情况）进行变化。我们的统计分析显示，PDF和功率谱与所谓的随机-δN算法大致一致。此外，“三次”情况还表现出一个特征上限，这在我们之前的工作中发现，它抑制了PBH的形成，同时可能影响暗物质团块的形成。此外，我们采用欧拉特征作为拓扑诊断工具，以识别瀑布场的结构以及曲率扰动的结构。我们发现，拓扑缺陷，如域墙（n=1）、宇宙弦（n=2）和单极子（n=3），在膨胀过程中通过随机噪声重新连接成更细的结构，使它们的相关长度远小于临界点的哈勃尺度，这与直觉相反。欧拉特征也暗示了曲率扰动的全球结构，尽管我们无法确定这些结构是否由于域墙引起，因为弦（n=2）和单极子（n=3）并未留下这样的结构。曲率扰动的全球结构将为早期宇宙的物理提供新的探测手段。

英文摘要：

We investigate the spatial profile of the curvature perturbation generated in multi-waterfall hybrid inflation models, which are known to produce various topological defects. Using the lattice simulation code STOchastic LAttice Simulation, based on the stochastic formalism of inflation, we analyse six cases by varying the number of waterfall fields $n$ and the functional form of the inflaton potential (``Quadratic'' and ``Cubic'' cases). Our statistical analysis shows that the probability density functions (PDFs) and power spectra are broadly consistent with the so-called stochastic-$δN$ algorithm. The ``Cubic'' case also exhibits a characteristic upper bound in the PDF, as discovered in our previous work, that suppresses \acl{PBH} formation while potentially affecting halo formation. Furthermore, we employ the Euler characteristic as a topological diagnostic tool to identify the structures of the waterfall fields as well as the curvature perturbation. We find that the topological defects, such as domain walls ($n=1$), cosmic strings ($n=2$), and monopoles ($n=3$), are reconnected during inflation into finer structures by the stochastic noise, making their correlation lengths much smaller than the Hubble scale at the critical point of the waterfall phase transition counterintuitively. The Euler characteristic also implies global structures of the curvature perturbation for $n=1$, though we do not conclude if they are due to the domain wall, because neither the strings ($n=2$) nor monopoles ($n=3$) leave such structures. The global structures of the curvature perturbation will provide a novel probe for the physics of the early universe.

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