Large scale perturbations in the open universe.
Large scale perturbations in the open universe.
复制标题
开放宇宙中的大规模扰动。
DOI：
10.1103/physrevd.52.3338
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Andrzei Woszczyna
中科院分区：
文献类型：
--
作者：
D. Lyth;Andrzei Woszczyna
当考虑开放(Omega<；1)宇宙中的微扰时，宇宙学家只保留次曲率模(定义为以曲率尺度为单位的本征值小于-1的拉普拉斯模，而超曲率模的本征值在-1和0之间)。近半个世纪以来，数学家们已经知道，必须包括所有的模才能生成最一般的齐次高斯随机场，尽管任何平方可积函数都可以仅使用子曲率模来生成。前者的数学对象，而不是后者，是与物理应用相关的对象。这里用物理学家可以理解的语言解释了数学。然后指出，如果微扰起源于标量场的真空涨落，则自然界中将不存在超曲率模。最后考虑了任何超曲率贡献对CMB的影响，推广了Grishchuk和Zeldovich在1978年给出的分析。并给出了估算效果的公式。与欧米茄=1的情况相比，该效应对所有多极都有贡献，而不仅仅是对四极。重要的是，通过对公式进行数值评估，找出它是否与数据具有相同的L相关性。
When considering perturbations in an open (Omega<1) universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than -1 in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between -1 and 0). Mathematicians have known for almost half a century that all modes must be included to generate the most general HOMOGENEOUS GAUSSIAN RANDOM FIELD, despite the fact that any square integrable FUNCTION can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. The mathematics is here explained in a language accessible to physicists. Then it is pointed out that if the perturbations originate as a vacuum fluctuation of a scalar field there will be no super-curvature modes in nature. Finally the effect on the cmb of any super-curvature contribution is considered, which generalizes to Omega<1 the analysis given by Grishchuk and Zeldovich in 1978. A formula is given, which is used to estimate the effect. In contrast with the case Omega=1, the effect contributes to all multipoles, not just to the quadrupole. It is important to find out whether it has the same l dependence as the data, by evaluating the formula numerically.