标题： 开放宇宙中大角度宇宙微波背景各向异性 显示英文标题

标题： Large-Angle Cosmic Microwave Background Anisotropies in an Open Universe

摘要： 如果宇宙是开放的，可以通过宇宙微波背景（CMB）的大角度涨落探测大于曲率尺度的尺度。 我们考虑原初绝热扰动，并讨论在体积、波长和拉普拉斯算子本征值方面为幂律的功率谱。 计算了CMB的大角度各向异性。 幅度通常随着$\Omega$的减小而增加，但随着$h$的增大而减小。 有趣的是，对于所有三种假设，相对于小于曲率尺度的各向异性，大于曲率尺度的各向异性被抑制。 具有$0.2<\Omega h<0.3$的模型与COBE和特内里费探测的CMB涨落以及星系巡天中星系计数涨落的幅度和谱相容。 这些模型的COBE归一化得到$\sigma_8\simeq 0.5-0.7$。 当将具有较小$\Omega h$值的模型归一化到COBE时，为了与$8/h$Mpc尺度上的观测星系计数相容，需要超过2的偏差因子。 要求宇宙年龄超过10 Gyr意味着$\Omega>0.25$，而要求宇宙年龄超过13 Gyr意味着$\Omega>0.35$。 与平坦宇宙情况下各向异性仅来自Sachs-Wolfe公式中的最后散射项不同，大角度各向异性主要来自在$z<1/\Omega$处的势起伏衰减。 因此，如果宇宙是开放的，COBE检测到的涨落是在中等红移处产生的，而不是在$z\sim 1300$处。 显示英文摘要

摘要： If the Universe is open, scales larger than the curvature scale may be probed by large-angle fluctuations in the cosmic microwave background (CMB). We consider primordial adiabatic perturbations and discuss power spectra that are power laws in volume, wavelength, and eigenvalue of the Laplace operator. The resulting large-angle anisotropies of the CMB are computed. The amplitude generally increases as $\Omega$ is decreased, but decreases as $h$ is increased. Interestingly enough, for all three ansatzes, anisotropies on angular scales larger than the curvature scale are suppressed relative to the anisotropies on scales smaller than the curvature scale. Models with $0.2<\Omega h<0.3$ appear compatible with CMB fluctuations detected by COBE and Tenerife and with the amplitude and spectrum of fluctuations of galaxy counts in galaxy surveys. COBE normalization for these models yields $\sigma_8\simeq 0.5-0.7$. Models with smaller values of $\Omega h$ when normalized to COBE require bias factors in excess of 2 to be compatible with the observed galaxy counts on the $8/h$ Mpc scale. Requiring that the age of the universe exceed 10 Gyr implies that $\Omega>0.25$, while requiring that the age exceed 13 Gyr implies that $\Omega>0.35$. Unlike in the flat-Universe case where the anisotropy comes only from the last-scattering term in the Sachs-Wolfe formula, large-angle anisotropies come primarily from the decay of potential fluctuations at $z<1/\Omega$. Thus, if the Universe is open, COBE has been detecting fluctuations produced at moderate redshift rather than at $z\sim 1300$.