用BOSS DR12星系样本探索宇宙均匀性
Exploring cosmic homogeneity with the BOSS DR12 galaxy sample
摘要：
在这项研究中，我们使用BOSS光谱巡天的CMASS星系样本探测宇宙大尺度结构（LSS）向宇宙均匀性的转变，该样本覆盖了迄今为止最大的有效体积，$0.43 \leq z \leq 0.7$的$3\ h^{-3}\ \mathrm{Gpc}^3$。我们研究了尺度计数的领域，$\mathcal{N}(<r)$和分形相关维，$\mathcal{D}_2(r)$，评估宇宙的均匀性尺度使用$Landy\ \&\ Szalay$启发估计。将过渡到同质性的尺度定义为$\mathcal{D}_2(r)$在$1\%$内达到3的尺度，即$r>\mathcal{R}_H$的$\mathcal{D}_2(r)>2.97$，我们发现$\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$在百分比水平上与$Λ$ CDM模型$\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$的预测一致。由于调查的大宇宙深度，我们调查的红移演化的过渡到均匀的规模，并发现与$Λ$ CDM预测协议。最后，我们发现，$\mathcal{D}_2$是兼容的$3$在规模大于$300\ h^{-1}\ $ Mpc的所有红移箱。这些结果巩固了宇宙学原理，并代表了$ΛCDM$模型的精确一致性检验。
英文摘要：
In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}(<r)$, and the fractal correlation dimension, $\mathcal{D}_2(r)$, to assess the homogeneity scale of the universe using a $Landy\ \&\ Szalay$ inspired estimator. Defining the scale of transition to homogeneity as the scale at which $\mathcal{D}_2(r)$ reaches 3 within $1\%$, i.e. $\mathcal{D}_2(r)>2.97$ for $r>\mathcal{R}_H$, we find $\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $Λ$CDM model $\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $Λ$CDM prediction. Finally, we find that $\mathcal{D}_2$ is compatible with $3$ at scales larger than $300\ h^{-1}\ $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $ΛCDM$ model.
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