缺陷网络演化的物理和不变模型
Physical and invariant models for defect network evolution
摘要：
我们重新审视速度依赖的单尺度模型的拓扑缺陷的演变，并提出了一个新的替代配方的物理（而不是不变的）特征长度尺度。虽然这两种方法是等效的（正如我们明确证明的那样），但在研究超相对论性缺陷的演化时，新方法特别相关。此外，两者的比较提供了进一步的洞察模型的两个唯象参数，$c$相关的能量损失和$k$相关的曲率的缺陷的解释。作为新公式的相关性的一个例证，我们用它来研究宇宙弦和畴壁网络在收缩宇宙中的演化。我们发现，这些网络是超相对论性和保形收缩，与物理长度尺度行为为$L_{ph}\propto a$和密度为$ρ\propto a^{-4}$（在辐射流体）在这两种情况下。另一方面，速度和不变长度分别表现为$(γv)\propto a^{-n}$和$L_{inv}\propto a^{\frac{4}{4-n}}$，其中$n$是缺陷世界表的维数。最后，我们还研究了另一种摩擦占主导地位的情况下，并表明，拉伸和基布尔政权确定的情况下，膨胀的宇宙也可以发生收缩的。
英文摘要：
We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are equivalent (as we explicitly demonstrate), the new one is particularly relevant when studying the evolution of ultra-relativistic defects. Moreover, a comparison of the two provides further insight on the interpretation of the model's two phenomenological parameters, $c$ related to energy losses and $k$ related to the curvature of the defects. As an illustration of the relevance of the new formulation, we use it to study the evolution of cosmic string and domain wall networks in contracting universes. We show that these networks are ultra-relativistic and conformally contracted, with the physical length scale behaving as $L_{ph}\propto a$ and the density as $ρ\propto a^{-4}$ (as in a radiation fluid) in both cases. On the other hand the velocity and invariant length respectively behave as $(γv)\propto a^{-n}$ and $L_{inv}\propto a^{\frac{4}{4-n}}$, where $n$ is the number of dimensions of the defect's worldsheet. Finally we also study an alternative friction-dominated scenario and show that the stretching and Kibble regimes identified in the case of expanding universes can also occur for contracting ones.
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