宇宙弦演化的結構性質

Abstract

我們使用吳俊輝教授提供的高解析度 (1024^3格點數) 宇宙弦模擬數據分析非膨脹宇宙中宇宙弦之碎形維度以及其他結構性質。宇宙弦的形狀可以利用碎形維度 d 描述，即宇宙弦的長度 L 和兩端點距離R 的關係。我們確認了碎形維度在小尺度趨近於 1，和大尺度趨近 2。我們也計算了宇宙弦的功率譜、Unequal Time Correlator (UETC)、長宇宙弦 (Long Strings)的能量密度 (ρ_∞) 和長宇宙弦轉移到 Small Loops 的能量密度轉換率 (X_L)。我們將這些結果和膨脹宇宙中的結果做比較，發現兩者在功率譜、UETC方面有很相似的特徵。我也研究了兩者在其他方面的關係。

We analyzed the fractal dimension and other structural properties of cosmic strings in a non-expanding universe, using the data of 1024^3 in resolution simulated by Jiun-Huei Porty Wu. The structure of cosmic strings can be characterized by the fractal dimension d, which relates the sectional string length (L) to the distance between the ends of the section (R). We show that the fractal dimension approaches one on small scales and approaches two on large scales. This is consistent with the theory and other studies[1]. We also studied the power spectra, the unequal time correlator (UETC), the long string’s energy density (ρ_∞), and its energy transfer rate to small loops (X_L). We compared our results with those in an expanding universe[5]. We found that they share similar features in power spectra and UETC. We also investigated the relationship between our results and those in an expanding universe[5].