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arXiv 0709.0875gr-qcastro-ph
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确定宇宙的度量标准:稳定性,准确性和一致性

Determining the metric of the Cosmos: stability, accuracy, and consistency

M. L. McClure, Charles Hellaby

摘要:

爱因斯坦场方程的最终应用是从宇宙的物质含量经验地确定宇宙的几何形状,而不是简单地假设宇宙可以用所有尺度上的均匀模型来表示。选择LTB模型作为开发早期阶段最方便的非均质模型,最近使用完美的测试数据验证了数据简化程序。在这里,我们模拟观测的不确定性,并改善以前的数值方案,以确保它将可用于与实际数据,只要观测调查是足够深和完整的。有两个区域需要特殊处理-原点和面积半径的最大值。为了使原点附近的数值误差最小化,我们使用LTB级数展开来提供积分微分方程的初始值。我们还使用了一种改进的方法来匹配的数值积分的级数展开,桥接区域半径的最大值附近的区域。由于封闭在最大的质量服从一个特定的关系,我们表明,它是可能的,以纠正固定的系统误差的距离尺度或红移空间的质量密度,这样的积分值是一致的数据在最大值。

英文摘要:

The ultimate application of Einstein's field equations is to empirically determine the geometry of the Universe from its matter content, rather than simply assuming the Universe can be represented by a homogeneous model on all scales. Choosing an LTB model as the most convenient inhomogeneous model for the early stages of development, a data reduction procedure was recently validated using perfect test data. Here we simulate observational uncertainties and improve the previous numerical scheme to ensure that it will be usable with real data as soon as observational surveys are sufficiently deep and complete. Two regions require special treatment--the origin and the maximum in the areal radius. To minimize numerical errors near the origin, we use an LTB series expansion to provide the initial values for integrating the differential equations. We also use an improved method to match the numerical integration to the series expansion that bridges the region near the maximum in the areal radius. Because the mass enclosed within the maximum obeys a specific relationship, we show that it is possible to correct for a fixed systematic error in either the distance scale or the redshift-space mass density, such that the integrated values are consistent with the data at the maximum.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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