Topological defects are a fossil relic of early Universe phase transitions, with cosmic strings being the best motivated example. While in most cases one studies Nambu-Goto or Abelian-Higgs strings, one also expects that cosmologically realistic strings should have additional degrees of freedom in their world sheets, one specific example being superstrings from type IIB superstring theory. Here we continue the scientific exploitation of our recently developed multi-graphics processing unit field-theory cosmic strings code to study the evolution of $\mathrm{U}(1)\times \mathrm{U}(1)$ multitension networks, which are a numerically convenient proxy: these contain two lowest-tension strings networks able to interact and form bound states, providing a convenient first approximation to the behavior expected from cosmic superstrings. We start with a discussion of our code validation, including a comparison of the evolution of these networks under three different assumptions: physical evolution (using the true equations of motion), the constant comoving width assumption (frequently used in the literature) and also the numerically convenient core growth case. We rely on the largest field-theory simulations of this model so far, specifically ${4096}^3$, $\mathrm{\Delta }x=0.5$ boxes. We present robust evidence of scaling for the lightest strings, measured through a complete and self-consistent set of correlation length and velocity diagnostics. We also find a linearly growing average length of the bound state segments, consistent with a scaling behavior. (In previously reported lower-resolution simulations, such behavior had only been identified with carefully engineered initial conditions, rich in those segments.) Finally, while we see no evidence of a large population of bound states forming at early stages of the network evolution, we do present tentative evidence for an asymptotic constant value of the fraction of bound states, with this value being different in the radiation and the matter eras. Our work demonstrates that our graphics processing unit-accelerated field-theory code can by successfully extended beyond the simple Abelian-Higgs approximation, and enables future detailed studies of realistic string networks and of their observational signatures.

中文翻译：

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高分辨率U(1)×U(1)模拟中的多张力弦

拓扑缺陷是早期宇宙相变的化石遗迹，宇宙弦是最好的例子。虽然在大多数情况下，有人研究 Nambu-Goto 或 Abelian-Higgs 弦，但也有人期望宇宙学现实的弦在其世界表中应该有额外的自由度，一个具体的例子是 IIB 型超弦理论中的超弦。在这里，我们继续对我们最近开发的多图形处理单元场论宇宙弦代码进行科学开发，以研究$\mathrm{ü}(1)\times \mathrm{ü}(1)$多重张力网络，这是一个数值上方便的代理：它们包含两个能够相互作用并形成束缚态的最低张力弦网络，为宇宙超弦预期的行为提供了一个方便的第一近似值。我们首先讨论我们的代码验证，包括在三种不同假设下比较这些网络的演化：物理演化（使用真实的运动方程）、恒定的共同移动宽度假设（在文献中经常使用）以及数值方便的核心增长案例。我们依赖于迄今为止对该模型最大的场论模拟，特别是${4096}^3$,$\mathrm{\Delta }X=0.5$盒子。我们提供了最轻弦缩放的有力证据，通过一组完整且自洽的相关长度和速度诊断来测量。我们还发现绑定状态段的平均长度呈线性增长，与缩放行为一致。（在先前报道的低分辨率模拟中，这种行为只有在精心设计的初始条件下才被识别出来，在这些片段中很丰富。）最后，虽然我们没有看到在网络演化的早期阶段形成大量束缚态的证据，我们确实提供了关于束缚态分数的渐近常数值的初步证据，该值在辐射和物质时代是不同的。