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arXiv 1107.4433astro-ph.CO
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具有非线性不均匀性的Λ CDM宇宙学中的红移和距离

Redshift and distances in a ΛCDM cosmology with non-linear inhomogeneities

Nikolai Meures, Marco Bruni

摘要:

受精密宇宙学的曙光和即将到来的高精度和体积星系调查的财富的启发,在本文中,我们研究了不均匀性对光在平坦的Λ CDM背景中传播的影响。为此,我们使用爱因斯坦方程的精确解(Meures & Bruni 2011),其中,从小的波动开始,不均匀性从标准增长模式产生并变得非线性。虽然这些模型中的物质分布必然是理想化的,但仍然有足够的自由来假设沿着视线的任意初始密度分布。因此,我们可以对各种尺寸和分布的过密度和空隙进行建模,例如,单谐波正弦模式、耦合模式和Λ CDM背景中的更一般的分布。我们的模型允许光传播问题的精确处理,因此结果不受近似和明确的影响。沿着视线与密度不均匀性的平均尺度小于哈勃半径,我们发现距离红移关系偏离弗里德曼-勒梅特-罗伯逊-沃克(FLRW)的结果可以忽略不计。相反,如果我们沿着与背景不具有相同平均密度的视线观察,我们会发现FLRW距离红移关系有很大的偏差。因此,如果我们沿着通常比宇宙平均密度更大或更小的视线进行观测,可能会在宇宙学观测的分析中引入一个可能的大系统,例如超新星。反过来,这可能导致错误的参数估计:即使宇宙学原理是有效的,在非均匀宇宙中识别真实的FLRW背景可能比通常假设的要困难。

英文摘要:

Motivated by the dawn of precision cosmology and the wealth of forthcoming high precision and volume galaxy surveys, in this paper we study the effects of inhomogeneities on light propagation in a flat ΛCDM background. To this end we use exact solutions of Einstein's equations (Meures & Bruni 2011) where, starting from small fluctuations, inhomogeneities arise from a standard growing mode and become non-linear. While the matter distribution in these models is necessarily idealised, there is still enough freedom to assume an arbitrary initial density profile along the line of sight. We can therefore model over-densities and voids of various sizes and distributions, e.g. single harmonic sinusoidal modes, coupled modes, and more general distributions in a ΛCDM background. Our models allow for an exact treatment of the light propagation problem, so that the results are unaffected by approximations and unambiguous. Along lines of sight with density inhomogeneities which average out on scales less than the Hubble radius, we find the distance redshift relation to diverge negligibly from the Friedmann-Lemaitre-Robertson-Walker (FLRW) result. On the contrary, if we observe along lines of sight which do not have the same average density as the background, we find large deviations from the FLRW distance redshift relation. Hence, a possibly large systematic might be introduced into the analysis of cosmological observations, e.g. supernovae, if we observe along lines of sight which are typically more or less dense than the average density of the Universe. In turn, this could lead to wrong parameter estimation: even if the Cosmological Principle is valid, the identification of the true FLRW background in an inhomogeneous universe maybe more difficult than usually assumed.

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