Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann–Lemaître–Robertson–Walker background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaître–Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

中文翻译：

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二阶微扰理论框架下的局部宇宙模型


最近，我们围绕任何充满尘埃物质和正宇宙学常数的 Friedmann-Lemaître-Robertson-Walker 背景构建了二阶宇宙学扰动理论的具体解。在本文中，我们使用来自银河系外距离数据库的星系 Cosmicflows-4 样本来约束这个度量张量。我们得到了局部物质分布和几何形状的近似值。我们对随机分布的模拟源的零测地线进行数值求解，并将该模型与在完美各向同性和均匀性假设下从观测中推断出的 Lemaître-Hubble 常数进行比较。我们总结了在哈勃张力背景下现实不均匀性对光度距离的影响，并讨论了我们方法的局限性。