标题： 紧致双曲三维空间的本征模式计算 显示英文标题

标题： Computation of eigenmodes on a compact hyperbolic 3-space

摘要： 宇宙微波背景（CMB）各向异性测量是发现宇宙非平凡全局拓扑的理想实验。 为了评估多重连接紧凑宇宙学模型中的CMB各向异性，需要计算拉普拉斯-贝尔特拉米算子的特征模。 利用直接边界元方法，我们在一个名为瑟斯顿流形的紧致双曲3维空间上数值获得了低阶特征模，该流形是已知紧致双曲3维流形中第二小的。 计算得到的特征模用单位三维伪球面上的特征模展开。 我们数值发现，对于低阶特征模，展开系数表现为高斯伪随机数。 假设高斯伪随机性是紧致双曲空间的普遍性质，则观测到的CMB涨落的高斯性可以部分归因于展开系数的高斯伪随机性。 显示英文摘要

摘要： Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct boundary element method, we numerically obtain the low-lying eigenmodes on a compact hyperbolic 3-space called the Thurston manifold which is the second smallest in the known compact hyperbolic 3-manifolds. The computed eigenmodes are expanded in terms of eigenmodes on the unit three-dimensional pseudosphere. We numerically find that the expansion coefficients behave as Gaussian pseudo-random numbers for low-lying eigenmodes. The observed gaussianity in the CMB fluctuations can partially be attributed to the Gaussian pseudo-randomness of the expansion coefficients assuming that the Gaussian pseudo-randomness is the universal property of the compact hyperbolic spaces.