哈勃麻烦还是哈勃泡泡？
Hubble trouble or Hubble bubble?
摘要：
最近对低红移超新星（SN）的分析增加了从低和高红移观测（如宇宙微波背景（CMB）辐射）估计的$H_0$值之间的明显张力。与此同时，其他的观测结果也提供了证据，证明存在着向不同方向延伸的局部径向不均匀性，最大红移可达$0.07$。用于SN校准的造父变星中，约有$40\%$直接受到影响，因为它们位于这些不均匀性的方向上。我们导出了一个新的简单的公式，它直接关系到光度距离的密度对比度，它不涉及任何度规扰动。然后我们用它来发展一种新的反演方法，从红移未校正的观测光度距离相对于基于大尺度观测获得的宇宙学参数的$ΛCDM$预测的偏差来重建密度场的密度。反演方法证实了存在的不均匀性，其影响以前没有考虑在内，因为$2M++$密度场图用于获得特殊的速度红移校正的$z\leq 0.06$，这是不是一个足够大的规模来检测存在的不均匀性延伸到$z=0.07$。不均匀性不影响高红移光度距离，因为体积平均密度对比度渐近趋于零，使得从CMB观测获得的$H_0^{CMB}$的值对任何局部结构不敏感。该反演方法为在只有SN数据的情况下重建高红移密度场提供了一种独特的工具，特别是可以将密度场相对于宇宙的平均大尺度密度进行正确的归一化。
英文摘要：
The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of $H_0$ estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about $0.07$. About $40\%$ of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the $ΛCDM$ prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the $2M++$ density field maps used to obtain the peculiar velocity for redshift correction were for $z\leq 0.06$, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to $z=0.07$. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of $H_0^{CMB}$ obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.
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