宇宙弦產⽣的宇宙微波背景B模偏振

Cosmic Microwave Background B-mode Polarization Induced by Cosmic Strings

葉佳隆(Jia-Long Johnny Yeh)

指導教授 ： 吳俊輝

國立臺灣大學/理學院/物理學研究所/博士(2017年)

https://doi.org/10.6342/NTU201702172

摘要

我們使⽤⾼解析度的宇宙弦模擬，計算宇宙微波背景輻射的圖在宇 宙弦的重⼒透鏡效應之下，所產⽣的影響。

我們藉由⽩化宇宙弦重⼒透鏡效應後的圖， 可以直接從⾁眼辨認 出宇宙弦所產⽣的⾮⾼斯訊號。搭配閔可夫斯基泛函 (Minkowski functionals) 去估計宇宙弦的線密度，我們利⽤頻域法 (frequentist approach) 提供實驗理想狀況下要觀測宇宙弦所需要達到的解析度。

在宇宙弦的模擬中，根基於 Smith-Vilenkin 演算法，我們提出了新 的實做⽅法，增進原本由吳俊輝教授寫的平空間宇宙弦模擬的資料結 構以及記憶體管理，減少了所需要使⽤的記憶體，達到了⽬前已知全 世界最⼤的平空間宇宙弦模擬。

並且我們進⼀步從宇宙弦會隨宇宙膨脹縮放 (scaling) 的性質，提供 了⼀個從平空間到膨脹空間的外插⽅法，讓我們可以藉由平空間的模 擬，外插到膨脹空間的模擬。藉由這個外插法，我們⾄少可以⽐⼀般 膨脹空間宇宙弦的模擬節省⼗倍以上的時間。

關鍵字

宇宙弦 ； 宇宙微波背景輻射 ； B模偏震 ； 重⼒透鏡效應 ； ⾮⾼斯

並列摘要

We use high-resolution simulations to simulate the cosmic microwave background (CMB) maps and their power spectra induced by the gravitational lensing from cosmic strings. We use the signal-whitening method to identify the non-Gaussian features and estimate the string linear density with Minkowski functionals. We further employ frequentist approach to analyze the ideal detectability including instrumental effect. We also provide a new formalism based on the Smith-Vilenkin algorithm in flat spacetime and optimize the simulation code first written by Prof. Jiun-Huei Proty Wu. Based on a new method for saving the computation memory, we successfully deliver the largest simulation of cosmic-string evolution to date. By considering the scaling properties of the string networks, we present a feasible way to extrapolate the evolutionary history of cosmic-string networks in a flat spacetime to that in an expanding spacetime, which is known to be at least ten times more time-consuming.

並列關鍵字

cosmic strings ； cosmic microwave background ； b-mode polarization ； gravitational lensing ； non-Gaussianity

參考文獻

[1] Christophe Ringeval. Cosmic Strings and Their Induced Non-Gaussianities in the Cosmic Microwave Background. Advances in Astronomy, 2010:1–28, may 2010.

doi:10.6342/NTU201702172 [65] Mark Hindmarsh. Small Scale Microwave Background Fluctuations from Cosmic Strings. The Astrophysical Journal, 431:534–542, 1994.

[2] Jose J. Blanco-Pillado, Ken D. Olum, and Benjamin Shlaer. Large parallel cosmic string simulations: New results on loop production. Physical Review D, 83(8): 083514, apr 2011.

[5] Planck Collaboration. Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics, page 20, 2015.

[6] Ruth Durrer. The Cosmic Microwave Background. CAMBRIDGE, 2008.