标题： 宇宙学中过去光锥之间的尺度相关距离泛函 显示英文标题

标题： A Scale-Dependent Distance Functional between Past Light Cones in Cosmology

摘要： 我们讨论了一种严格的过程，用于量化我们过去的光锥与基准弗里德曼-勒梅特-罗伯逊-沃尔克时空的过去光锥之间的差异，该时空在标准$\Lambda\mathrm{CDM}$场景中对宇宙数据的大尺度描述进行建模。 这一结果是通过利用我们最近引入的过去光锥之间的尺度依赖距离泛函实现的。 我们将这种调和映射类型的泛函表示为表征我们过去光锥上实际测量的物理量，即面积距离和引力透镜畸变，并且还解决了光锥奇点存在的非常微妙的问题。 这种分析效果非常好，似乎消除了在将我们过去光锥的实际几何结构与所选基准FLRW光锥的几何结构进行比较时遇到的若干困难。 我们还讨论了从FLRW几何的角度来看，这个距离泛函可以被解释为一种尺度依赖的有效场，即预均匀场，这可能在选择最符合观测数据的FLRW模型时具有相关性。 显示英文摘要

摘要： We discuss a rigorous procedure for quantifying the difference between our past lightcone and the past lightcone of the fiducial Friedmann-Lemaitre-Robertson-Walker spacetime modeling the large-scale description of cosmological data in the standard $\Lambda\mathrm{CDM}$ scenario. This result is made possible by exploiting the scale-dependent distance functional between past lightcones recently introduced by us. We express this harmonic map type functional in terms of the physical quantities that characterize the actual measurements along our past lightcone, namely the area distance and the lensing distortion, also addressing the very delicate problem of the presence of lightcone caustics. This analysis works beautifully and seems to remove several of the difficulties encountered in comparing the actual geometry of our past lightcone with the geometry of the fiducial FLRW lightcone of choice. We also discuss how, from the point of view of the FLRW geometry, this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity field, that may be of relevance in selecting the FLRW model that best fits the observational data.