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arXiv 1111.6396astro-ph.CO
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具有宇宙学常数的平坦宇宙学中光度距离的解析近似

An analytical approximation of the luminosity distance in flat cosmologies with a cosmological constant

Masaru Adachi, Masumi Kasai

摘要:

本文给出了一个在含有尘埃和宇宙学常数的空间平坦宇宙学中光度距离的解析近似公式。在我们的公式中,除了总因子外,非零宇宙学常数的影响可以简单地用有理函数表示。给出了空束情况下的Dyer-Roeder距离和从红移$z_1$到$z_2$的广义角直径距离的近似公式,这些公式在分析引力透镜效应时特别有用。我们的公式是广泛适用的密度参数和红移的范围内具有足够小的不确定性。特别地,在密度参数$0.3 \leq Ω_{\rm m} \leq 1$和红移$0.03 \leq z \leq 1000$的范围内,我们公式计算的光度距离的相对误差总是小于Wickramasinghe和Ukwatta(2010)最近的工作.因此,我们希望我们的公式将是一个有效的和有用的工具,探索各种问题的观测宇宙学。

英文摘要:

We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is written simply in terms of a rational function. We also show the approximate formulae for the Dyer-Roeder distance (empty beam case) and the generalized angular diameter distance from redshift $z_1$ to $z_2$, which are particularly useful in analyzing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter $0.3 \leq Ω_{\rm m} \leq 1$ and redshift $0.03 \leq z \leq 1000$, the relative error for the luminosity distance by our formula is always smaller than that of the recent work by Wickramasinghe and Ukwatta (2010). Hence, we hope that our formulae will be an efficient and useful tool for exploring various problems in observational cosmology.

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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